Banerjee, who sprang a surprise by proposing Prime Minister Manmohan Singh's name for the President's post on Wednesday, was scheduled to take a flight to Kolkata on Thursday afternoon but her close aides said she is not leaving the capital.
Asked about the possibility of Banerjee meeting Singh, Railway Minister Mukul Roy said, "The question does not arise."
Sources said Banerjee will stay put in the capital and may have discussions with some leaders on the issue.
Trinamool sources said the PM had invited Banerjee for a meeting on Wednesday but it did not take place as the schedule was not finalised.
The PM's invitation to Banerjee came on a day before she met Congress chief Sonia Gandhi.
After the meeting with Gandhi, Banerjee said Congress' choice for the top post is Finance Minister Pranab Mukherjee and Vice President Hamid Ansari.
Later, she and Yadav had a meeting during which they came up with the name of the Prime Minister and former President A P J Abdul Kalam and Lok Sabha Speaker Somntah Chatterjee.