The 29-year-old midfielder was limited to 18 Bundesliga appearances for Dortmund this season, scoring just two goals.
Since joining the club from Real Madrid in 2013, he has made 121 appearances for the club, but has only managed to score on eight occasions.
Şahin's contract expires in twelve months, and Fanatik and Sport Italia (via Football ITALIA) both report that Dortmund have decided not to offer him a fresh deal.
The decision now means that the Turkish international is free to leave the club for a reduced fee this summer, with Liverpool - a club where Şahin previously spent time on loan - are reportedly keen on a move.
However, the Reds have already recruited two midfield reinforcements this season, with Fabinho and Naby Keïta both linking up with the squad this summer.
Roma and Galatasary have registered their interest in Şahin following his latest contractual development, giving the midfielder plenty of options for the summer.
His potential future teammate, Naby Keïta, recently picked up a calf injury whilst on international duty with Guinea, and is receiving treatment from the medical staff at RB Leipzig. His move to Liverpool will be made official on 1 July.
Şahin could replace German international Emre Can, who has been heavily linked with a move to Serie A champions Juventus.