The striker is approaching the end of back-to-back season-long loan spells at Portman Road, with this his third stint in total, knowing his three-year contract with the Scottish Premier League giants expires this summer.
And Murphy, 29, is keen to become a permanent addition to Town's squad, although he admits his focus is currently on securing Championship football for the Suffolk outfit.
"I won't be going back to Celtic," Murphy told the club's official website. "My contract is up at the end of the season and then I will become a free agent and we will see what happens after that.
"Everyone knows how much I like it at Ipswich - I'm one of the long-serving players having been here three times on loan.
"The priority is to see Ipswich stay up this season and nothing will be looked at until that can be achieved but after that then I hope something can be sorted out because obviously I'd like to stay here. It's a great football club."
- Sports & Recreation