The 29-year-old Celtic striker, who has spent the last two seasons on loan at Portman Road, is out of contract at the end of the current campaign.
Murphy, who joined Celtic from Sunderland in 2010, has claimed that he would accept a drop in wages to become an Ipswich player on a permanent basis.
"I wanted to go and play football at Celtic - I thought I would play football there, I took a pay cut and I would do it again to play," he told BBC Radio Suffolk.
"My contract at Celtic is up in June. After that we'll see what happens. I'd like to stay [at Ipswich]. It's obvious now, I've been here so long I feel like I'm part of the furniture.
"I'll talk to the gaffer (Mick McCarthy) - it's his call. When we're safe we'll talk about it."
Murphy has scored six goals in 35 appearances this season.