The 21-year-old made just three La Liga starts in 2013-14, with a further 20 appearances coming off the bench.
Despite his lack of playing time, Morata still managed eight league goals, but the Spaniard's chances of breaking into a forward line boasting Cristiano Ronaldo, Angel di Maria, Gareth Bale and Karim Benzema remain limited.
On Monday, coach Ancelotti, who guided the club to their 10th European Cup triumph last month, hinted that Real would be open to letting Morata leave the club.
"The footballer wants to find an opportunity to have more minutes and the club agrees with this," he said.
"If you are looking for a chance to play it would be good to have opportunities for a year.
"If Morata leaves we will have to think about a replacement with similar characteristics."
