A second term for incumbent Ansari appears certain, with several parties in the alliance and outside giving their support to his candidature in the August 7 election.
Key UPA constituent Trinamool Congress, however, may propose the name of former West Bengal Governor Gopalkrishna Gandhi as Mamata Banerjee is not quite enthusiastic about Ansari's candidature for second term.
The last day for filing nomination for the vice presidential election is July 20, a day after the presidential poll.
The UPA is comfortably placed in the electoral college comprising 790 members of Parliament. With the backing of outside supporters like Samajwadi Party and Bahujan Samaj Party and others, the UPA has nearly 500 MPs on its side.
Prime Minister Manmohan Singh, who has stepped up efforts to seek a consensus on Ansari's candidature by talking to leaders of non-UPA parties like the Janata Dal-Secular, Communist Party of India-Marxist and the CPI, spoke to Trinamool chief and West Bengal Chief Minister Mamata Banerjee on Wednesday seeking their support for Ansari.
The prime minister is learnt to have informally solicited the support of the JD-U for the vice presidential election amid indications that the National Democratic Alliance partner might find it difficult to oppose Ansari's candidature having earlier described him a "good" candidate for Presidentship. The JD-U is supporting the UPA's presidential candidate Pranab Mukherjee.
JD-U chief Sharad Yadav, however, remained non-committal on the issue saying his party will take a decision after deliberations in the NDA and talking to other opposition parties.
Banerjee, who has been keeping away from Delhi after the Congress rejected her choice of presidential candidates and is yet to declare her party's support to Mukherjee, has deputed Railway Minister Mukul Roy for the meeting.
Roy may propose Gandhi's name along with that of Krishna Bose, former Lok Sabha member and niece of Subhas Chandra Bose, as the Trinamool choice for the vice-president's post.
UPA sources maintained that Ansari, who missed the bus in the presidential nomination, remained the only choice for the ruling alliance for the vice-president's post.
Ansari is considered a "safe" choice even though the Trinamool Congress with its 28 MPs in both Houses of Parliament has so far given no indication of backing him.
NCP sources said the prime minister had spoken to party chief Sharad Pawar twice and only Ansari's name cropped up during the discussions.
CPM general secretary Prakash Karat has already said he favoured a non-Congress person for the post of vice-president and had conveyed the same to the prime minister.
"We have told the prime minister that we would like to have a person who does not belong to Congress party to be the vice-president," Karat had said.
Karat said the vice-presidential candidate should have "stature and a distinguished background".
Incidentally, the Left parties, which were key outside supporters of the UPA-I, had proposed the name of Ansari for vice-presidentship in 2007.
Saturday's meeting could be utilised by the UPA top brass to take stock of the situation on the presidential election as well.
Meanwhile, UPA Chairperson Sonia Gandhi will host a lunch for MPs of the UPA and those backing Mukherjee's candidature on July 18, a day ahead of the presidential election.