The former Liverpool youngster, who joined the Whites in 2010 as part of the deal that saw Paul Konchesky make the switch to Anfield, made his Fulham debut as a substitute in Saturday's victory over Norwich.
Cottagers boss Martin Jol told the Fulham Chronicle: "We have to protect the club's younger players and Alex only has a year left.
"He's shown he can play at Championship level. He did well there [at Watford]. They are raving about him.
"He has shown he will give competition for [Kerim] Frei and Clint [Dempsey]."