The 31-year-old midfielder is available as a free agent following his release by Leeds United.
He saw out the 2013/14 season on loan at Portman Road and had hoped to have done enough to earn a permanent stay.
Ipswich boss Mick McCarthy is yet to make an approach, though, and Green admits he is keeping all of his options open as a result.
The Republic of Ireland international said in the Green Un: “My agent has spoken to Mick but no offer has been made yet.
“I really enjoyed it at Ipswich and I could see myself moving down there, but you never know what is going to happen.
“I have spoken to a couple of other teams but nothing is certain yet. It’s a case of wait and see, but Ipswich would definitely be up there at the top of my list.
“Mick was brilliant and was a big attraction in me going down there, he knows how to get teams out of this division.
“He also creates a great team spirit and I didn’t want the season to end.”
While prepared to bide his time, Green admits he is hoping to have something in place by the time teams return for pre-season training at the start of July.
He added: “You don’t want to be missing much of pre-season as it’s such an important part of the build-up to the season.
“I remember missing one before and you are playing catch-up all the time.
“It would be nice to get something sorted in the next couple of weeks.”