The midfielder linked up with the Sky Bet Championship outfit in November on a short-term agreement which has been lengthened until the end of the season.
The 32-year-old has quickly become an important squad player at Portman Road, with his experience a useful weapon in Mick McCarthy's arsenal.
He will, however, drop back into the free agent pool in the summer unless fresh terms are put to him.
Hunt plans to do all he can to ensure that he is not cast aside, with the Republic of Ireland international enjoying life in Suffolk with an ambitious outfit.
He told Ipswich's official matchday programme: "I'm very happy here at Ipswich and I love the area so, all being well, I can hopefully do enough to persuade the manager that I deserve a longer deal.
"That's the aim for me and if that happens, then I will get the family over here and settle in Suffolk.
"The short-term contract I first signed was really a case of 'what if' and it allowed the gaffer to have a look at me, and me to have a look at Ipswich and see if things could go further.
"There weren't any politics involved or anything like that and knowing him and TC (Terry Connor) from Wolves like I did, I knew he would be totally honest and straight down the line with me.
"Obviously I knew I had to prove myself to get into the team and thankfully I managed to get my foot in the door and I've done pretty well since I've been in.
"Now the aim is to keep working hard until the end of the season and try and get the team into the play-offs. After that, then we can hopefully sort out a longer deal."