The 29-year-old midfielder joined Inter on a free transfer from local rivals AC Milan and has grown in stature with the Serie A giants.
He has six goals in 14 Serie A appearances this season and is considered one of the best midfielders in Italy.
Saudi Arabian clubs were interested in him last summer but Inter were in no mood to listen to offers for the midfielder.
According to Italian sports daily Tuttosport (via Tutto Mercato), Chelsea and Liverpool have their eyes on the 29-year-old midfielder.
There is serious interest in him from the Premier League, but Chelsea and Liverpool are the two clubs who are keen on the Turkey international.
He still has a contract until 2027 with Inter and the Nerazzurri are in no mood to lose him yet.
It remains to be seen whether Chelsea and Liverpool are prepared to make a move for the Inter star in January or next summer.
