The Irishman made 25 appearances for Town since joining from Bohemians last year but has been out with a broken ankle since Christmas.
But manager Paul Jewell has revealed that fellow keeper Arran Lee-Barrett and midfielder Colin Healy have verbally agreed one-year deals to stay at Portman Road.
He said: "Colin and Aran are staying which is good news.
"But Brian Murphy has turned down the offer we made him which is his choice.
"He has left the club and we wish him well."
Source: PA
Source: PA