Murphy, 32, hit 27 goals for Ipswich as the Tractor Boys reached the play-offs, only to be beaten in the semi-finals by their fierce East Anglian rivals Norwich City.
Now, former Sunderland striker Murphy could be in demand this summer, with Wales Online reporting that he is Cardiff City's top target, and they could bid as much as £4m to lure him to South Wales.
Ipswich and manager Mick McCarthy will surely try to keep the Irishman at Portman Road, but an offer of that magnitude for a player over 30 may be hard to turn down.
It's a remarkable turnaround from Murphy, who was essentially on the scrapheap at Celtic just two years ago, having failed to make an impact in Glasgow.
Murphy joined the Bhoys from Sunderland in 2010 and whilst he scored three goals in 21 games in his first season, he spent the next two out on loan at Ipswich before making his move permanent in 2013.
With 27 goals to his name this season, Murphy has shown Celtic what they are missing - and just two years after being released by Celtic, Murphy could now be sold for £4m. Few Bhoys fans could have expected that when Murphy left in 2013.