Besides Sawant, the names of BJP MLA and former state health minister Vishwajit Rane, and Himachal Pradesh Governor Rajendra Arlekar, who hails from Goa, are being discussed for the CM's post.
The BJP won 20 out of the total 40 seats in the Goa elections and secured the support of MGP and three Independents.
Chodankar was at the helm of affairs of the Congress during the recent elections held for the 40-member Goa Assembly.
TMC national general secretary Abhishek Banerjee, said that the party will convene a series of internal review meetings to introspect its role in Goa.
Congress in more mess? Three days over since Goa poll results, party yet to decide its legislature leader
According to sources, the Goa Congress unit has not held a single meeting after it failed to reach the majority mark of 21 in the 40-member Assembly.
Rane has been projecting himself as a contender for the post of Goa chief minister after the BJP won 20 of the total 40 seats in the recent elections, sources said.
Out of the total of 20 seats, the grand old party won only five, after having secured victory in 10 of those five years ago. In North Goa, too, the Congress tally fell from seven to six.
Sawant met Governor P S Sreedharan Pillai at the Raj Bhavan around noon and submitted his resignation.
Some newly-elected BJP MLAs in Goa are against accepting the support of the Maharashtrawadi Gomantak Party, sources said.
Some of the BJP MLAs expressed confidence that the saffron wave will also sweep Jharkhand in the next assembly polls.
Talking to reporters after the meeting, state Revenue Minister Jeniffer Monserratte said the cabinet will also be dissolved on Monday.
The victory margin remained below the 100-mark in two of these constituencies in the coastal state, where the assembly polls were held on February 14 and the results were declared on Thursday.
BJP’s Goa in-charge Devendra Fadnavis claimed the party has got a support letter from Maharashtrawadi Gomantak Party which has two MLAs.
TMC's show in the Goa assembly election failed to match the noise it made while entering the poll fray, with no seat to show for its efforts.
Goa Chief Minister Pramod Sawant has been able to deliver victory for the party in the assembly elections in the coastal state.