Murphy moved to Parkhead in a £800,000 deal from Sunderland in the summer of 2010 but has struggled to hold down a first-team place north of the border.
The 30-year-old has made just nine starts for the SPL champions in three years, spending the majority of the last two seasons on loan at Portman Road.
With his contract set to expire at the end of the month, Murphy admits he is keen to seal a permanent move to the Tractor Boys, even if it means a drop in wages.
"In a perfect world I would love to stay on at Ipswich," said the Republic of Ireland forward. "It won't bother me to take a pay cut because that's what I did to join Celtic.
"For me it's all about playing and if it wasn't I would still be at Sunderland picking up my money."