Gandhi has been at the forefront of evolving a consensus among opposition parties for a joint candidate "acceptable to all".
The Congress chief has already met a number of leaders, including Nitish Kumar and Sharad Yadav, both of the JD(U), Sharad Pawar of the NCP and Left leaders Sitaram Yechury and D Raja.
Gandhi is likely to meet other opposition leaders like West Bengal Chief Minister and Trinamool Congress leader Mamata Banerjee, BSP supremo Mayawati, besides M K Stalin of the DMK in the next few days, the sources said.
Sources said the opposition is trying to put up a united face and jointly fight the presidential poll even though the numbers have tilted in favour of the NDA after Uttar Pradesh Assembly election results.
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Parleys are also being held among leaders of other opposition parties.
The presidential election has to be held before July 24 when Mukherjee's term ends.
He had taken over the post in July 2012, defeating the NDA candidate late P A Sangma.
There has been a sudden flurry of activity by the opposition to forge a strong alliance to take on the Narendra Modi-led BJP after its recent winning streak in several states.
The BJP currently has governments in 13 states and is a junior partner in the ruling alliances in Jammu and Kashmir and Andhra Pradesh.
Some feel that the united face of the opposition for contesting the presidential elections may well turn out to be a precursor to an anti-NDA front ahead of the 2019 Lok Sabha election.