The Spanish giants remain reluctant to sell their young striker, but have decided they would be willing to sanction a loan move for a £1.7million fee.
The Spain Under-21 international was originally told he would be going nowhere by Real Madrid boss Carlo Ancelotti.
But Morata has since revealed his desire to play regular first team football for the second half of the season, following reported interest from both Arsenal and Liverpool.
“It’s important to have a proper role in the team,” Morata explained.
“I’ve been at Real Madrid my whole life and I’ve been a Real Madrid fan since I was a boy. I will be all my life, but it’s important to have an important role.
“If the moment comes that I don’t, I will look at other options. Staying at Real Madrid is complicated. Playing five or 10 minutes is okay if you accept it.
“You have the chance to get on the pitch and try to change a game in a short space of time. Every minute in football is gold.”
Arsene Wenger is desperate to sign a new striker this month to add cover for the injured Theo Walcott, although he looks set to face a battle for Morata’s services with Brendan Rodgers, who is keen to add more firepower to help the Reds fight for a top four finish.