Finance minister Pranab Mukherjee is likely to meet Prime Minister Manmohan Singh over the Presidential elections at 12 noon in New Delhi on Friday.
Mukherjee will also attend the UPA meeting scheduled on Friday over the same issue in new Delhi at 4pm.
The Congress Core Group, which met at the residence of Singh on Thursday, is believed to have decided to put forward Mukherjee's name for the coveted post.
The latest development comes a day after West Bengal chief minister and Trinamool Congress (TMC) chief Mamata Banerjee warned the Centre, and indirectly hinted at toppling the government.
"We want to be in the UPA. If they don't want us in the government, that choice is with the Congress," she told media here after meeting Samajwadi Party (SP) chief Mulayam Singh Yadav.
Banerjee also said APJ Kalam was her first choice for the president's post.
"Our formidable candidate is Kalam. They rejected the name of other candidates. So now Kalam is our candidate. We will be very happy if Kalam contest the elections and he will win the elections," said Banerjee.
"Every party should support Kalam. It should have nothing to do with politics. It is good if there is consensus. If there were no consensus, then we would appeal to electorates to vote according to their conscience. I have no information about it," she added, while urging the leaders of various other political outfits to back Kalam's candidature.
Both Mamata and Mulayam had on Wednesday evening announced the names of former president APJ Abdul Kalam, Prime Minister Manmohan Singh and former Lok Sabha speaker Somnath Chatterjee as their preferred choices for the July 19 presidential poll. The two leaders also rejected the names of finance minister Pranab Mukherjee and vice president Mohammad Hamid Ansari as suggested by Sonia Gandhi.
The Congress has ruled out Prime Minister Manmohan Singh's name as a Presidential candidate.
"He will remain our PM till 2014. We cannot afford to spare Manmohan Singh as PM," said party spokesperson Janardhan Dwivedi.
Dwivedi also said that the names of former Lok Sabha speaker Somnath Chatterjee and former president APJ Abdul Kalam as proposed by Mamata and Mulayam were not acceptable to the Congress.
Trinamool Congress, with 19 members in the Lok Sabha, is the largest constituent of UPA after the Congress. On the other hand, the Samajwadi Party, which has 22 members in the Lok Sabha, is an outside supporter of the ruling alliance.
President Pratibha Devisingh Patil's term ends on July 24.