"Nobody has sought my resignation," Trivedi told reporters outside Parliament scotching reports that he had quit after Mamata wrote to the Prime Minister last night to replace him.
He said it was his duty to ensure passage of the Rail Budget which he had presented on Wednesday in Parliament.
"It is my duty to get the Rail Budget passed and this is my prime duty," he said.
At the same time, he added "The moment my leader Mamata Banerjee or the Prime Minister asks me, I will resign".
Finance Minister Pranab Mukherjee earlier told the Lok Sabha that Trivedi had not resigned.
He said a communication from Banerjee was received late last night and "as and when a decision will be taken, the House will be informed."
Mukherjee did not divulge details of the communication and his remarks came after opposition uproar over the issue of reported resignation of Trivedi as railway minister.
Trivedi, who attended Lok Sabha today during the Question Hour, has justified his Budget in which he had proposed a hike in passenger fare which earned him the wrath of his party chief and West Bengal Chief Minister.