Mr Parrikar, 62, has already informed Governor Mridula Sinha that he has been advised to travel overseas for "specialised expert treatment" for his "medical condition".
"I have been advised by an expert team of doctors in Goa as well as in Mumbai ... to travel overseas for specialist expert treatment of my medical condition. As such, I am likely to leave for the US," Mr Parrikar wrote to the Governor in his letter, dated March 5.
The Chief Minister has been in and out of hospitals since February 15. On Monday evening, he left for Mumbai's Lilavati Hospital where he is being treated for "mild pancreatitis", according to an official statement.
"I am thankful for all. In the last 15 days you have been praying for me and you have blessed me because of which I got well and to get fully cured I may go abroad," Mr Parrikar said in a video message.
"The way you have prayed for me and blessed me, I hope to get the same thing during my treatment there. I expect that you all will allow me a leave for some days from the state for the treatment," he said.
Mr Parrikar had also met Goa chief secretary and the director general of police, before leaving the coastal state.
Mr Parrikar was admitted to the Lilavati Hospital on February 15 where he received treatment for a pancreatic ailment.
He was discharged on February 22, and on the same day attended a session of the Goa Legislative Assembly, where he presented the budget and made a brief speech.
Three days later, Mr Parrikar was admitted to the Goa Medical College and Hospital after he suffered mild dehydration. He was discharged from the hospital on March 1.
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