Manchester United and Chelsea have both been monitoring the Spanish striker, as they seek to strengthen their respective attacks.
Jose Mourinho has been handed a £200million transfer kitty to revive United, although Zlatan Ibrahimovic appears set to be his first striker acquisition.
And according to Spanish paper Marca, no firm decision has been taken on Morata’s future.
It is believed Real are confident Morata could end up staying.
It is also thought that the club are demanding around £60million for the player.
Atletico have also been exploring the option of bringing Diego Costa back to Spain.
Antonio Conte is expected to carry out a serious overhaul of his squad, and a striker has been identified as a priority.
Morata is currently the joint top scorer at Euro 2016 with Wales’ Gareth Bale, who have both scored three goals so far at the tournament.
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