Everton, Arsenal and Liverpool are amongst the teams interested in signing the 24-year-old, although Sport Bild has claimed AC Milan, Schalke and Borussia Dortmund are also in the running.
Demirbay is contracted to Hoffenheim until 2021, but he has a release clause of £29 million.
After spending time with Borussia Dortmund II in Germany’s third tier, Demirbay joined Hamburg in 2013.
He subsequently moved to Kaiserslautern on a season long loan in 2014 and went on to make 23 appearances for the club in all competitions.
Demirbay was loaned out again the following August to Fortuna Dusseldorf for the season and 11 goals in 26 games was enough to secure a move to Hoffenheim in June 2016.