The Republic of Ireland international's future was the subject of conjecture in the winter transfer window, with the midfielder keen to move to the Premier League.
Hunt opted to sign a new contract with the Royals, but the club ultimately failed to gain promotion from the Championship.
Media reports claim Everton are lining up an offer for Hunt and the 27-year-old intends to seal a transfer away from Reading this summer.
He told Sky Sports News: "My own situation is that I am happy at Reading, but in terms of my future, I've been loyal to Reading, maybe a fresh start would be good for me and the club.
"I think me and the club agree it is time for a fresh start. I don't know about that (Everton). I can't talk about other clubs."
Meanwhile, Brynjar Gunnarsson's future at Reading is also in doubt despite being offered fresh terms by the club.
Gunnarsson's agent, Olafur Gardarsson, said: "He hasn't rejected the offer but he is mulling over his options.
"He's got the offer of a one-year contract and he is considering that and also other offers from clubs in the Championship."
Coca Cola Ch'ship 2009/10 Win Outright: Reading 12/1
Source: Team_Talk