Mr Parrikar was sworn-in as Goa Chief Minister on March 14 this year. He has to get elected to the Assembly within six months of taking charge as the CM.
Mr Parrikar resigned as the Defence Minister after the BJP formed the government in Goa following the assembly elections in February.
BJP legislators Siddharth Kuncolienkar (Panaji) and Nilesh Cabral (Curchorem), have volunteered to resign from their seats to pave way for Mr Parrikar's entry in the House.
"Whichever constituency Parrikar is going to contest, Congress will field its candidate against him. The party has decided that it will defeat Parrikar in the by-election," Goa Congress LegislatureParty (CLP) leader Chandrakant Kavlekar told PTI.
The BJP is yet to decide which constituency Mr Parrikar will contest from.
He said all his legislators are united and have vowed to defeat Mr Parrikar, whose party according to them, stole the mandate given to Congress by the people in the Assembly polls.
In the 40-member Goa House, Congress had won 17 seats and BJP 13. However, the latter formed the government after cobbling up support from regional parties and independents. Congress had not fielded its candidate from Panaji constituency in the Assembly election and had extended support to United Goans' party nominee Atanasio Monserratte, who contested against BJP's Kuncolienkar, and lost.
The BJP is likely to meet this week to decide on the constituency from which Mr Parrikar will contest the bypoll.