Zlatan Ibrahimovic is set to leave Manchester United next month on a free transfer after the club chose not to activate the additional year in his contract.
The Swede has since been linked with a move to MLS, following the likes of Steven Gerrard and David Beckham to LA Galaxy.
However, Spanish outlet Don Balon claim the 36-year-old does not want to bow out in America and is keen to stay in Europe.
The report says Ibrahimovic was hopeful his agent Mino Raiola could engineer a move to Real Madrid but the deal has fallen flat.
It is said Ibrahimovic was hopeful of replacing Alvaro Morata who is tipped to join Manchester United this summer.
The former Malmo man was reportedly asking for wages of around £165,000 a week but Real are not interested.
The La Liga champions are instead focusing all their efforts on securing a deal for Monaco teenager Kylian Mbappe.
Ibrahimovic has, however, received an offer from Real’s La Liga rivals Valencia.
But the striker is said to have turned down their offer and is holding out for a top club to come in for him.
Ibrahimovic previously spent two years in Spain with Barcelona but left the club due to his differences with former manager Pep Guardiola.
He made just 47 appearances for the Catalan side, scoring 22 goals and providing 14 assists in all competitions.
During his time at the Nou Camp he won the La Liga title and two Spanish cups.