Congress sources said Gandhi is understood to have conveyed to several leaders that it is time for the grand old party to look for a new chief.
Faced with a colossal electoral defeat, the Congress was on Monday riven by internal turmoil with Rahul Gandhi insisting on quitting as party president while its governments in Rajasthan and Karnataka teetered on the brink.
In the midst of the disquiet, several state Congress chiefs, including Punjab's Sunil Jakhar, Jharkhand's Ajoy Kumar and Assam's Ripun Bora, also offered to resign following the party's drubbing in the elections, party insiders said.
Congress sources said Gandhi is insisting on resigning his post and is understood to have conveyed to several leaders that it is time for the grand old party to look for a new chief.
The Congress won only 52 out of 542 parliamentary seats in the Lok Sabha polls, just six more than its 2014 tally. The party could not open its account in 18 states and Union Territories.
Taking responsibility for the defeat, Gandhi on Saturday offered to resign as party president at a meeting of the Congress Working Committee (CWC), the highest decision-making body of the party, but it was 'unanimously rejected'.
At the CWC meeting, Gandhi accused three senior leaders -- Ashok Gehlot, Kamal Nath and P Chidambaram -- of placing their sons above the party.
His sister Priyanka Gandhi Vadra said the entire top brass of the party left Rahul Gandhi alone to fight it out against Prime Minister Narendra Modi.
As the party grapples with a severe existential crisis, its governments in both Karnataka and Rajasthan face a tough time with reports suggesting the Bharatiya Janata Party may try to wrest power in both states.
It is learnt that Congress legislators Ramesh Jarkiholi and Dr Sudhakar visited BJP leader S M Krishna's residence in Bengaluru on Sunday along with several other BJP leaders and they are understood to have deliberated on dethroning the incumbent dispensation.
Sources said a number of Congress legislators in Karnataka are understood to be unhappy over the party's electoral loss.
In Rajasthan, there have been reports of internal turmoil with several ministers demanding fixing of accountability and seeking action against those responsible for the poll debacle in the state.
The Congress drew a blank in Rajasthan as the National Democratic Alliance won all 25 seats.
In Karnataka, where it formed a government with the Janata Dal-Secular in May last year, the Congress managed to win only one Lok Sabha seat out of 28.
The party was crushed in most of the 29 states, including Madhya Pradesh, Rajasthan and Chhattisgarh, where it had defeated BJP in the assembly polls in December.
As crisis beset the opposition party, its chief spokesperson Randeep Surjewala on Monday urged everyone to respect the sanctity of the CWC meeting and asked the media not to fall into the trap of 'conjectures, insinuations, gossip and rumour-mongering'.
Surjewala said it is a democratic forum for exchange of ideas and taking corrective action. It was a 'closed-door' meeting and any speculation about it was unwarranted and uncalled for, he added.
He was reacting to news reports about happenings at the May 25 meeting, the first of the CWC after the Congress's humiliating defeat in the parliamentary polls.
"The Congress party expects everyone, including the media, to respect the sanctity of a closed-door meeting of the CWC. Various conjectures, speculation, insinuations, assumptions, gossip and rumour-mongering in a section of the media is uncalled for and unwarranted.
"The CWC held a collective deliberation on the performance of the party, the challenges before it as also the way ahead, instead of casting aspersions on the role or conduct of any specific individual.
"The gist of the deliberations was made public in the CWC resolution of May 25, 2019," the Congress leader said in a statement.