Reports continue to suggest that the Spain Under-21 international could be heading out of Santiago Bernabeu during the winter transfer window.
Real boss Carlo Ancelotti has expressed a desire to keep the youngster in the Spanish capital, but is also aware that he cannot guarantee him game time.
A lack of activity has alerted the likes of Arsenal to his potential availability, with the Gunners believed to be leading the chase for the 21-year-old's services as they seek to bolster their attacking options.
Morata is paying little attention to the gossip at present, but concedes that he will need to consider his future if is unable to hold down a regular role at Real.
He told Minuto 116: "Real Madrid have been my team since I was little and will be all my life, but I think the important thing is to have a relevant role in the team.
"If I ever feel that's not the case, I would look at other options. In football, it's very difficult to stay at the top and even more so in a team like Real.
"Moving up to the first team is tricky, not everyone deals with it well. If you learn how to handle it, you realise the value of every minute.
"Maybe in five or 10 minutes you have to go on and be decisive in a game. In football every minute is golden."