Adams said the club's chief executive Peter Storrie was already in negotiations with several clubs about Defoe who joined the club eleven months ago for £9m from Tottenham.
Portsmouth are sending in a doctor to check on Defoe, 26, who missed last year's FA Cup final victory over Cardiff because he had been cup-tied in one of his last appearances for Tottenham.
Adams said: "Jermain is not very well and a doctor is going round to his house to assess him.
"Peter Storrie had a meeting with him last Wednesday, which I sat in on, and he expressed a desire to leave. I think Peter is talking to a few clubs.
"The final decision will be mine and I have a price in mind of what I think he is worth."
Portsmouth still owe around £4m to Tottenham for the original sale and Adams hinted that he could force Defoe to sit out the remainder of his two and a half year contract.
"I left Jermain out of games against Liverpool and Arsenal and he was very upset. If those decisions I made tactically have influenced his decision to leave then I am sorry.
"He is a super player and a great goalscorer and I have not made up my mind whether I will sell him or not. I have to make a call on that like I did with Lassana Diarra when Real Madrid came knocking.
"If I wanted to play him against Bristol City I would have done because he is still a Portsmouth player but it looks as if that decision has been taken out of my hands by his illness."
Martin Cranie makes his first appearance of the season in a weakened Portsmouth side in which Peter Crouch will play as the sole striker.