With his vast political experience, Pawar is being seen as a natural choice for such an opposition grouping while Kumar is a Dalit leader and hails from the Congress, which is the biggest non-Bharatiya Janata Party (BJP).
Yadav is a veteran socialist leader with extensive parliamentary experience.
Gandhi, a grandson of Mahatma Gandhi and respected scholar, enjoys cross-party appeal. Trinamool Congress (TMC) is keen on his name, sources said.
Gandhi PTI that he has been approached by some opposition leaders but declined to name them.
Congress chief Sonia Gandhi, JD(U) chief and Bihar Chief Minister Nitish Kumar, Communist Party of India (Marxist)'s (CPI(M)) Sitaram Yechury, CPI's D Raja, Yadav as well as other opposition leaders have held talks to evolve a consensus for pitting a joint candidate against the NDA's choice.
Efforts are also on to widen the opposition alliance by roping in TMC, Naveen Patnaik-led Bharatiya Janata Dal (BJD) and several regional parties from the southern states.
The electoral college clearly favours the NDA choice for the top constitutional post, more so after the BJP's emphatic win in Uttar Pradesh. Though it is still short of a clear majority but its leaders are confident of getting the required support.
Many opposition leaders believe that putting up joint candidate irrespective of the outcome of the election may also mark the coming together of a larger alliance against the BJP in the run-up to the 2019 Lok Sabha polls.
The electoral college for the presidential polls has a total of 11,04,546 votes with the BJP-led NDA tally currently standing at about 5.38 lakh votes.
The ruling alliance also received a boost on Wednesday with the YSR Congress Party Chief Jagan Mohan Reddy pledging his party's support to it. It also hopes to get support from All India Anna Dravida Munnetra Kazhagam (AIADMK) factions.