The ruling Congress party was due to meet its coalition allies on Friday to finalise its presidential candidate.
Party sources have said that Mukherjee is the front-runner for the largely ceremonial position, although a key ally has rejected his candidacy, raising questions about whether Congress has the votes it needs to get its man into the presidential palace.
There was no immediate comment from Mukherjee's office on the reports.
TV channels report the former UP chief minister, Mulayam Singh Yadav, has reached an agreement with the UPA to support finance minister Pranab Mukherjee, but Trinamool Congress leader Mamata Banerjee claims he is going to support APJ Abdul Kalam. Yadav has not spoken and his party is making cautious statements.
The Samajwadi Party on Friday said that the party did not want early elections and did not want to topple the government.
Samajwadi Party leader Ram Gopal Yadav also said that the party will not join the UPA government. On being asked if Kalam was the joint candidate of the two parties, Ram Gopal said, "'Hamara' could also mean 'mera'," indicating only Mamata was committing on Kalam till now.
(With Reuters inputs)