Party all India general secretary Mukul Roy was also at the meeting, but left earlier.
The three leaders were believed to have discussed developments after Trivedi, who is in the line of fire of the Trinamool Congress, during the day turned down his party's directive to quit his post insisting that he wanted it in writing from the party chief.
Trivedi also said he would reply to the debate on the Railway budget in Parliament.
Firm on the removal Trivedi, the Trinamool supremo asserted that it was time for Prime Minister Manmohan Singh to act on her plea to replace Trivedi with Mukul Roy.
"I have already said whatever I have had to say. Now the government has to decide. Mukul Roy will be our candidate for the Railway minister," Mamata said during the filing of nominations for Rajya Sabha elections by Roy, the Union minister of state for Shipping, and three others.