The name of Krishna Bose, former Lok Sabha member and niece of Netaji Subhash Chandra Bose, is also being floated by the party, though Gandhi could be their prime choice, party sources said.
Prime Minister Manmohan Singh last night spoke to Trinamool Congress chief Mamata Banerjee, stepping up efforts to drum up support for Hamid Ansari for a second tenure in the post of Vice President, elections to which are scheduled for August 7.
However, there is strong speculation that Railway Minister Mukul Roy, who has been asked by Banerjee to attend the UPA meeting on Saturday, may propose that Gandhi be made the nominee of the ruling coalition for Vice President.
On the Presidential election, Trinamool Congress has said its would announce the party's strategy three days ahead of the poll slated for July 19.
Trinamool Congress has maintained silence on whether it would support UPA nominee Pranab Mukherjee or abstain.
The party has asked all its MPs and MLAs to be present in Kolkata from July 16 onwards.
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If it decides to vote, all the electors would exercise their franchise in Kolkata and has sought permission for this from the Secretary General of Rajya Sabha, who is the Returning Officer, the sources said.
They said the Trinamool Parliamentary Party would meet on July 17 in the eastern metropolis to decide on the Presidential poll.
Last evening, Singh spoke to the West Chief Minister, who was on a tour of North Bengal, after which Trinamool Congress decided to attend the July 14 meeting to decide on the Vice Presidential poll candidate. The last date for nomination for the Vice President election is July 20.