The Republic of Ireland international was signed by former manager Mark Robins from Coventry City a year ago.
Murphy, 33, has had to make do with four appearances, two of them in the Capital One Cup.
Last week he joined Chesterfield in an emergency loan deal and featured in Sunday’s 3-0 League I play-off semi-final, second leg loss at Preston North End.
Earlier in the season, he was linked with former club Scunthorpe United, now managed by Robins.
Joe Murphy for Huddersfield Town
Current Town boss Chris Powell is reshaping his squad ahead of the 2015-16 Championship campaign.
And with a strict budget to adhere to, it could be that Murphy, who still has a year on his contract, moves on.
Born in Dublin, he began his career at Tranmere Rovers before a 2002 move to West Bromwich Albion.
He had a spell at Sunderland before joining Scunthorpe in 2006.
Murphy, who has two Republic of Ireland caps, played more than 200 times for the Iron, twice helping them win promotion from League I.
He was transferred to Coventry in 2011, and made 156 appearances over three seasons.