Isco is unhappy at Real Madrid and wants to quit this summer.
And, according to Spanish website Don Balon, Morat is helping him get ready for a switch to London.
It is claimed Morata has begun house hunting for his former team-mate.
Isco looks set to leave the Bernabeu in the summer with a host of Premier League clubs interested.
Manchester City were thought to be favourites to land the Spain star, but Manchester United and Chelsea appear ready for a transfer battle.
Isco, 25, has fallen down the pecking order at Madrid and is fed up after impressing last term.
He has been kept out of the team by Gareth Bale, Karim Benzema and Cristiano Ronaldo despite Real’s poor La Liga form.
And Florentino Perez looks set to embark on a huge overhaul this summer.
Reports have emerged saying up to 10 player could leave the club after a disappointing season.
Real sit third in La Liga and are already out of the title race as they trail Barcelona by 15 points.
Even second place Atletico are 10 points clear ahead of their meeting with Barcelona this weekend.
Their only hope of salvation lies in the Champions League where they lead PSG 3-1 ahead of the last-16 second leg.