The Republic of Ireland winger is the Tigers' most saleable asset despite a foot injury that could keep him out for the whole summer.
Hull rejected a £5million bid from Wolves in January but Hunt revealed he struck an agreement with chairman Adam Pearson that he would be allowed to leave if the club failed to stay in the Premier League.
Their relegation was confirmed on Monday and financial troubles mean Hull must slash their wage bill in preparation for Championship football.
With Hunt, whose contract runs until 2013, among their highest earners, a sale would appear to be in both parties' interests, and Wolves, Newcastle and West Brom are all thought to be tempted.
The 28-year-old told the Irish Herald: "I presume the club will want to sell me in terms of the overall financial structure. I didn't want to go. If we had stayed up I'd have been happy to stay ay Hull but we're not in the Premier League now and they may need to sell me.
"If I do move on, it will be with a clear conscience, and I can be honest about that. In January we had an agreement that they would sell me due to the financial situation that would arise from relegation.
"The chairman has been very good to me. He said once I gave my all for Hull he'd have no problem in honouring that agreement for me to go. I have done that, I have done well for Hull.
"Unfortunately, I haven't delivered as much as I'd like because we've been relegated."
Hunt, who joined Hull from Reading for an undisclosed fee last summer, also revealed the Tigers are prepared to accept less than the £5million Wolves offered in January.
"The club say they will be willing to sell me at a reduction of the price they'd have got for me in January," he added. "I have no idea what that reduction will be and if a club will come up with the money.
"All I can do is concentrate on getting fit and see what happens."