However, there is a section within the NDA, particularly the Janata Dal-United, which is of the view that a contest against Mukherjee should be avoided as there could be embarrassment for the coalition.
The NDA leaders will meet in New Delhi on Sunday to finalise the coalition's position on the issue.
Though there was no official word, all indications were that A P J Abdul Kalam, propped up by Trinamool Congress, may not after all enter the fray in view of the fact that there is no guarantee of victory.
Sensing the ground situation, Mamata launched a campaign in the social media, seeking support for Kalam.
Ahead of the NDA meeting, top leaders of the Bharatiya Janata Party -- L K Advani, Nitin Gadkari, Sushma Swaraj and Ananth Kumar -- met in New Delhi on Saturday night to firm up the party's stand on the issue with indications that they are not too enthusiastic about supporting the UPA nominee Pranab Mukherjee.
Sources in the BJP said there was a view in the party that there should be a contest, whether it is by backing P A Sangma, the nominee of the All India Anna Dravida Munnetra Kazhagam and the Biju Janata Dal, or by supporting Kalam, whose candidature is being pushed by Trinamool Congress.
With the possibility of Kalam contesting virtually ruled out, the NDA may plump for Sangma as it may help it win back allies like the AIADMK and BJD who were earlier part of the coalition.
Another view was that there could be a bonus if Mamata also backs Sangma given the current bitterness she harbours against Congress.
Interestingly, BJP member Ram Jethmalani tried to inject fresh element, saying he would contest against Mukherjee if the NDA chooses to support the UPA nominee because he failed to act against black money. The NDA fielding its own candidate was also not ruled out.
After the BJP core group meeting, Kumar said party leaders are in touch with their counterparts in the allied parties and "others". He said Advani, Gadkari and Swaraj have held telephonic talk with leaders of NDA allies to evolve a common position.
"We discussed the emerging situation in the context of Presidential poll... NDA leaders will meet tomorrow and take a final decision," Kumar the media but did not reply to questions as to whether any names were deliberated upon.
Sources in the JD-U said the party would favour a consensus around Mukherjee and feels a contest should be avoided as it could be embarrassing because neither has Kalam so far agreed to contest nor the NDA has the numbers.
JD-U chief Sharad Yadav met Shiromani Akali Dal leaders including Naresh Gujral after which he said NDA will take a collective decision on the matter on Sunday.
Gujral slammed attempts to drag Kalam's name in the Presidential race, saying it amounted to "demeaning and trivialising" Kalam as he has not given his consent for the same.
BJP sources said the party was in touch with Sangma as also Kalam besides AIADMK chief Jayalalithaa and BJD leader Naveen Patnaik. Meanwhile, there was pressure on Sangma, an NCP leader, from his party chief Sharad Pawar to withdraw from the race. Pawar hoped to convince Sangma.
Another party leader Praful Patel warned of action against Sangma if he does not withdraw.