The 23-year-old sealed a return to the Bernabeu after a fee of R500-million was agreed with Juventus on 21 June, bringing a close to two successful seasons in Italy's Serie A.
However, he could soon be on the move again if Chelsea decide to up their offer, with Real said to be holding out for a fee closer to R1,2-billion.
The Blues aren't the only Premier League side looking to sign Morata, though, as Arsenal have also been strongly credited with an interest in the striker.
Arsene Wenger's side will be able to offer Morata Champions League football, but the player's prime concern is playing regular first-team football next term.
"I want a team that makes me feel important and I would be ready to stay in Madrid to win my place," Morata told Spanish TV station Cuatro.
"I do not have to prove anything to anyone. I am a player of Real Madrid and they will decide if they want me, otherwise we will find another solution."