The 29-year-old midfielder will become a free agent at the end of the season and he is expected to leave the Bernabeu.
Spurs have previously been linked with the Spaniard in the January transfer window and according to the Daily Star, the Premier League giants could soon offer a contract to the attacker.
Real Madrid have reportedly stepped up their interest in Paris Saint-Germain’s Kylian Mbappe following the striker’s comments over his future.
The 22-year-old forward has confirmed that talks are underway regarding a new deal with the PSG, where he has claimed he is “very happy” as he looks to sign an extension past 2022.
The 29-year-old striker has been impressive in recent weeks with four goals in his last four top flight outings, but the Frenchman has now entered the final 18 months of his contract at the Emirates.
Despite playing a key role for the Reds since moving to Anfield in 2017, the Egyptian recently refused to rule out a move to either Madrid or Barcelona.
He still has two-and-a-half years left to run on his contract, though, and manager Jurgen Klopp has insisted that he remains relaxed over his future despite the ongoing rumours.