The experienced midfielder moved to Portman Road in February on a short-term loan agreement.
He had been deemed surplus to requirements by parent club Leeds United and will see his contract at Elland Road expire in the summer.
Having impressed during his time at Ipswich, there is every chance that Green will be back next season.
McCarthy will be leaving that door open, but will take a good look at the market before making a decision on the 31-year-old Republic of Ireland international.
He said in the Green Un following Saturday's 2-1 victory over Sheffield Wednesday: "I thought Greeny was outstanding - he was by far the best player on the park.
"I've just spoken to him and said 'keep in touch'. We're not going to sign him now, that's not going to be the case, but he's certainly given me a lot of food for thought in how he's played and how he's gone about his business. I think he's great and I really like him."
Green said: "No footballer looks forward to pre-season, but it would be great to come back here and be with the lads.
"There is a terrific team spirit here - a real togetherness with everyone pulling in the right direction. It all bodes well for Ipswich and I believe they can do even better next season and make that top six."
He added: "I enjoyed my first year at Leeds but the second didn't work out.
"For some strange reason I wasn't getting in the squad there, so coming here to trying and help Ipswich get into the play-offs has been enjoyable.
"The gaffer has given me a chance here and hopefully I have repaid his faith."