The rapidly approaching January transfer window will provide new Gers boss Giovanni van Bronckhorst with his first opportunity to start to reshape the squad at Ibrox.
And the Dutchman has taken note of Galatasaray star Morutan, according to Turkish outlet En Son Haber.
The 22-year-old, who is a Romania international, can operate as an attacking midfielder or a winger, and Rangers are impressed with his abilities.
Rangers are currently assessing how much money would be needed to sign the attacker, with a loan with an option to buy the formula that the Glasgow giants are likely to opt for.
However, Rangers could encounter difficulty convincing Galatasaray to let Morutan go.
While the Romanian has not been a regular starter under Galatasaray coach Fatih Terim, it is suggested that Terim is against seeing him depart.
The Galatasaray boss rates Morutan and values the qualities he provides.
Morutan has so far turned out in 18 games for Galatasaray so far this season, scoring three times and providing two assists.
He joined the Turkish giants from Steaua Bucharest last summer.
