The two would-be Dy CMs are Goa Forward Party chief Vijai Sardesai and Maharashtrawadi Gomantak Party MLA Sudin Dhavalikar.
Rane did not rule out the possibility of joining the BJP, saying 'all options are open'.
The BJP's victory in the Delhi Assembly elections has sparked speculation over who will lead the next government. Several prominent leaders, including Pravesh Verma, Ashish Sood, Pawan Sharma, Vijender Gupta, and Satish Upadhyay, are in the running for the chief minister's post. The party's national leadership is expected to make the final decision, leaving the contenders in a state of anticipation.
He said had the alliance with Goa Forward gone through, the Congress would have got majority in the state and that it was unfair to now make him a "villain".
Besides 11 members from BJP, three each from the Goa Forward Party, the MGP and independents supported Sawant during the head count conducted in the House.
Sawant, who took over as chief minister for the first time in March 2019, brought the BJP tantalizingly close to the simple majority mark of 21, defying pre-poll predictions of a hung assembly.
The discussions on the new Goa CM came to a halt after Maharashtrawadi Gomantak Party MLA Sudin Dhavalikar wanted to be the chief minister.
The lowest victory margin of 76 was recorded in St Andre constituency in North Goa, where Revolutionary Goans Party, a new political outfit in the state, made its debut by defeating BJP candidate and sitting MLA Francis Silveira. RGP candidate Viresh Borkar won the contest.
Prime Minister Modi and Defence Minister Rajnath Singh would be present at the function, a government spokesperson said.
The opposition Congress could muster only 16 votes against the government with one of its legislators absenting from the crucial floor test.
Incumbents Pushkar Singh Dhami and Pramod Sawant are the clear favourites but face some opposition
The vote value of an MLA is calculated on the basis of the total population of the state, based on the 1971 census.
Both the BJP and the Congress said they will seek support of the MGP in case they fall short of the majority mark of 21.
The move could be attributed to the withdrawal of support to the state government by the Nationalist Congress Party and some independent legislators.
The cabinet of the new government led by Rekha Gupta balances representation of all major communities that propelled the Bharatiya Janata Party to power in Delhi with a massive majority after over 26 years.
In the 2017 state assembly polls, the Congress had emerged as the single largest party by winning 17 seats.
While none of the five 'rebel' MLAs were available for comments, sources in the BJP claimed the legislators were in touch with them.
Chidambaram, who is the Congress' senior election observer for the assembly polls next year, asserted that the Trinamool Congress' entry into Goa "appears to be an imposition from the top that is based in West Bengal" and said he does not know the Mamata Banerjee-led party's motive in trying to start a unit in Goa by "encouraging defections" from other parties.
Goa Chief Minister Manohar Parrikar on Monday said the central government was responsible for illegal mining in the state as it gave environment clearances for the projects without verifying basic facts.
Goa Congress chief Subhash Shirodkar on Saturday resigned, owning responsibility for the party's defeat in the recently held Legislative Assembly election. Shirodkar handed his resignation to party president Sonia Gandhi in New Delhi. He and former chief minister Digambar Kamat were in Delhi to submit a report on the party's performance in Goa. Shirodkar had said two days ago that he would be stepping down, taking the responsibility for the drubbing.
"In all, 22 of us (including 18 MLAs) met party chief and presented our view that we have majority in the state assembly," Pratapsinh Rane said.
He said his supporters were apprehensive that joining TMC would invite the "outside party" to Goa which will split votes.
The draft will be examined, studied and discussed before it is tabled in the assembly on February 6, he said.
A condom ad campaign featuring Sunny Leone has offended Goa's politicians.
Goa Tourism Minister Dilip Parulekar told the state legislative assembly on Monday that the government is considering Playboy's proposal to set up a club at Candolim beach, while responding to a question by Bharatiya Janata Party legislator Michael Lobo on the floor of the House.
Several Bharatiya Janata Party-ruled states in the country, including Gujarat and Assam, have expressed their keenness to follow the Uttarakhand UCC as a model.
Goa Chief Minister Manohar Parrikar on Sunday inducted six more ministers in his Cabinet, including four legislators from the Bharatiya Janata Party.
Five Goa Congress MLAs, who went incommunicado a day before, attended the state assembly proceedings on the first day of the monsoon session on Monday, and claimed there was 'nothing wrong' in the opposition party.
Senior BJP leader and Patnagarh MLA KV Singh Deo and debutant from Nimapara assembly segment Pravati Parida took oath as deputy chief ministers.
As per the power-sharing arrangement, Goa Forward Party chief Vijai Sardesai and Maharashtrawadi Gomantak Party MLA Sudin Dhavalikar will be the deputy chief ministers.
former union minister Renuka Chowdhury said the mandate was given to the party and it was natural for its MLAs to feel bitter about not being able to form the government.
The five vacancies in Goa -- Taleigao, Cambarjua, Benaulim, Margao and Poinguinim -- have been caused following the resignation of incumbent members of Legislative Assembly in the month-long political drama.
The Congress and the Nationalist Congress Party will be forging an alliance for the forthcoming state legislative assembly elections in Goa, a senior NCP leader said on Wednesday. "The alliance will happen. The Congress and the NCP are both keen to have an alliance for Goa elections," NCP Goa Observer Bharati Chawan said. She also rubbished all the doubts raised in this regard by a few local leaders. Congress leaders had said that the party can go alone in the state.
Even as illegal purchase of land violating Foreign Exchange Management Act (FEMA) is haunting Goa government, an ad hoc committee was told that the state can restrict the sale of land to foreign nationals under Foreigners Rule, 1946.
Hit hard by defections in the last five years, the Congress in Goa on Friday made its candidates sign affidavits and take an oath of loyalty to the party in the presence of its senior leader Rahul Gandhi.
The seven-month-old Save Goa Front, a regional outfit launched by former Congressman Churchill Alemao, on Wednesday formally merged with the Congress party.
Goa Tourism Minister Dilip Parulekar has sought time to respond to the Calling Attention motion moved by Bharatiya Janata Party legislator Michael Lobo on the issue of Playboy Club, which has sought permission to open a branch in the state.
The two-time MLA from Sankhalim in North Goa, Sawant, who was speaker of the state assembly, is a dedicated Rashtriya Swayamsevak Sangh worker.
The numbers game seems weighed against Pratapsinh Rane.