The Championship pair both want to sign the 33-year-old.
The Championship pair both appear to be looking for the kind of striker that can inspire them back towards the top flight, and there are arguably few with better track records in the second tier than the 33-year-old.
Murphy has spent the majority of the last five seasons at Portman Road - his first two campaigns with the club were loan spells - and has gone on to score 67 league goals for the Tractor Boys, finishing as the top goalscorer in the division in 2015.
Despite his value to Mick McCarthy's side however, it is conceivable that Ipswich would not be completely against the idea of letting him leave this summer.
Daryl Murphy playing for the Republic of Ireland at Euro 2016
The Irish Sun reports that the forward - who featured for the Republic of Ireland at Euro 2016 - is about to enter the final year of his contract. Therefore, given his age and the fact that he was not quite as prolific last season, they may decide to let him go this summer rather than lose him for nothing next year, especially if they have any concerns over how much of a contribution he will be able to make this term.
However, it would obviously be a gamble if they did decide to allow him to leave for one of the two clubs reportedly chasing his signature, as they will know that he could well have the quality to strengthen their promotion bid while also potentially weakening Ipswich's own hopes of challenging for a top six spot.