The Celtic defender is due to return to the SPL club in the new year. He has made 11 appearances for Roy Keane`s side and is enjoying his time at Portman Road despite the current poor run of form.
Saturday's defeat at Preston was a sixth in a row in the league and O'Dea is eager to help Town get back on track.
"I'm really enjoying it here and I'd like to stay," the 23-year-old told the club's official website.
"I've not really thought about it too much though. It's down to other people to sort out but I'm certainly enjoying my football here.
"I think my time at Ipswich has helped me improve as a player and we have to see what happens over the next few weeks but it's not important at the moment, all I want to do is help the team get back up the table."