The Trinamool Congress has already announced its support for Singhvi's candidature. Singhvi is representing the party in the Supreme Court in some high-profile cases.
He also represents Karti Chidambaram, son of former finance minister P Chidambaram, in the INX Media case.
Congress President Rahul Gandhi approved the names of 10 party candidates. The last date for nominations is tomorrow.
The party cleared the names of Amee Yagnik and former Union minister Naranbhai Ratwa from Gujarat, Dhiraj Prasad Sahu from Jharkhand, and Rajmani Patel from Madhya Pradesh.
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The party has also nominated L Hanumanthaiah, Syed Naseer Hussain and G C Chandrasekhar from Karnataka, while Porika Balram Naik has been nominated to contest from Telangana.
The election is slated on March 23 and the results will be out on the same day after 5 PM.
The party has preferred local leaders in some key states which are going to polls later this year.