Spanish outlet Don Balon say the Premier League duo are ready to open talks about the forward if he asks to leave.
He was brought back to the Bernabeu from Juventus this summer after Real activated a buy-back clause.
He was expected to be sold on to the Premier League at a profit, however Zinedine Zidane wanted to keep him to provide competition for Karim Benzema.
Morata stayed in the Spanish capital but has remained largely on the bench.
Don Balon say Morata is unlikely to agitate for a move away but if the time comes Arsenal and Chelsea will be ready and waiting to bring him to the Premier League.
Real's formidable frontline of Cristiano Ronaldo, Benzema and Gareth Bale are too strong for Morata at the moment and that looks like continuing for the foreseeable future.
But the 23-year-old is expected to stay and fight for his spot. The only question is, how long for?
