Parrikar on Friday told reporters that he was formally invited by Modi to join his central cabinet and although he felt sad to leave Goa, he had decided to accept the offer because it was a matter of "national interest" and because "no one says no to a prime minister".
He is tipped to be sworn in as India's next union defence minister on Sunday.
The Bharatiya Janata Party (BJP) is also expected to announce a new chief minister for Goa after a meeting of party legislators around noon on Saturday.
The party's national observers Rajeev Pratap Rudy and B.S. Yeddyurappa will be present at the meeting in Goa to tide over the process of transition from Parrikar to the new chief minister.
Parrikar is tipped to be sworn in as India's next union defence minister
While current Health Minister Laxmikant Parsekar and Speaker Rajendra Arlekar are the top seeds for the post, Deputy Chief Minister Francis D'Souza put a spanner in the works late on Friday by insisting that he would not work under either of the two leaders because they were junior to him.
D'Souza, who claimed that 12 BJP as well as independent legislators were on the same page with him on the issue, however, was more receptive to the idea of union Minister for Tourism and Culture Shripad Naik being brought to state politics and appointed as chief minister.
Efforts by Parrikar to cajole D'Souza and get him to agree to either Parsekar and Arlekar did not bear fruit, even as the senior BJP leader tried to put a brave face through the embarrassment caused by D'Souza tantrum.
"I have tried my best, now it is up to the party to decide," Parrikar told reporters late Friday after a one-to-one meeting with D'Souza.
When asked who in his opinion could be his best successor as chief minister, Parrikar said: "Tomorrow (Saturday) at 1 o'clock on the 8th of November, you can ask."
On Monday, Parrikar is expected to fly to Lucknow in Uttar Pradesh where he will file his nomination papers to book passage to parliament through the Rajya Sabha.