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.
Chodankar was at the helm of affairs of the Congress during the recent elections held for the 40-member Goa Assembly.
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.
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.
CM Pramod Sawant was trailing in Sanquelim constituency, while health minister Vishwajit Rane, a prominent contender or the CM's post, was leading in Valpoi constituency.
MGP to emerge as kingmaker in Goa? BJP starts discussion with former ally as exit polls predict hung assembly in state
In 2019, when Pramod Sawant became the CM, two MGP ministers were dropped from the state cabinet. This time, the MGP contested the state Assembly elections in alliance with the Trinamool.
The party seems to have taken lessons from the 2017 Goa election, when slow decision-making by the leadership helped the BJP form government in the coastal state despite not having the numbers.
'Open to post-poll alliance with non-BJP parties': Congress extends olive braches to AAP, Trinamool ahead of Goa results
The Congress had contested the election in alliance with the Goa Forward Party. Besides, the Mamata Banerjee-led TMC had tied-up with the MGP, Goa's oldest regional outfit, before the polls.
The Grand Old Party is wary of a repeat of the 2017 situation when it emerged as the single largest party but was trumped by the BJP which cobbled together a coalition quicker.
The Congress had emerged as the largest party in the 2013 Assembly polls but the BJP managed to form a government will allies, following which several MLAs from the Congress switched over.
Chodankar had filed a disqualification petition against 10 party MLAs who switched over to the BJP in July 2019. Another petition was filed by MGP MLA Sudin Dhavalikar.