At a two-hour inconclusive meeting of the NDA, the JD(U) is believed to have disavoured a fight against Mukherjee because of his stature but BJP is said to have been keen on backing former Speaker P A Sangma, who has been propped up by BJD and AIADMK with an eye on the 2014 Lok Sabha polls.
After the meeting at BJP leader LK Advani's residence, from which BJP's oldest ideological ally Shiv Sena kept away, NDA convener Sharad Yadav merely said more discussions were needed to arrive at a right decision.
"The NDA meeting took place today. Various leaders put forth their views in detail. More discussions are required in this regard to arrive at the right decision.
"LK Advani will talk to Chief Ministers of NDA-ruled states and all others. NDA will meet sometime later again to take a decision in this regard. Those outside (Delhi) will also be consulted," Tadav told reporters after the meeting.
The JD(U), which shares power with BJP in Bihar, was clear that there is no strong purpose served by contesting against Mukherjee, a tall leader with vast experience in government and Parliament, and more so when the UPA has a clear edge in the electoral college.
However, BJP leaders including Advani and Sushma Swaraj are understood to have argued that Mukherjee should not go uncontested, especially in view of the Lok Sabha polls due two years hence.
The BJP is said to be keen on supporting Sangma so that the alliance could rope in parties like BJD and AIADMK that could be valuable in the next Lok Sabha elections.
While Yadav did make the point against contesting Mukherjee, he was not averse to going with the BJP should it persist with a fight in the Presidential election.
However, Shivanand Tiwari, the other JD-U leader, who is considered close to Bihar chief minister Nitish Kumar, strongly opposed a contest. This is seen as an attempt by Nitish Kumar to keep his options open.
Prime Minister Manmohan Singh and Mukherjee had called Kumar on Friday seeking JD(U)'s support for the UPA candidate.
BJP leaders remained tight-lipped after the meeting and downplayed any differences within the NDA, saying more consultations were required as it is a democratic alliance.
BJP leaders felt Advani should stay in touch with AIADMK chief Jayalalithaa and BJD chief Naveen Patnaik so that the options of a contest are still open.
Shiv Sena, the oldest ideological ally of the BJP, skipped the key meeting of alliance leaders here, triggering speculation the party was opposed to a fight due to lack of numbers.
"Shiv Sena chief Bal Thackerey will take a decision on the issue," said party leader Sanjay Raut, when asked about speculation that the Sena was against fielding any candidate against Pranab Mukherjee, UPAs Presidential nominee.
Shiv Sena had not backed former Vice President Bhairon Singh Shekhawat in the Presidential poll last time despite BJP and several others in the alliance supporting him.
At that time, it had backed Pratibha Patil--she being the first Maharashtrian to be nominated for the top post of President.