Brazil goalkeeper Julio Cesar has joined Benfica on a two-year deal after being released by QPR.
The 21-year-old will spend the whole fo the forthcoming season back in Spain after starting just twice in his first year at Anfield.
Liverpool paid a reported £6.8m for Alberto when he was bought from Sevilla last summer, but he was last seen in action in Janaury.
A club statement read: "Liverpool today confirmed that midfielder Luis Alberto has completed a season-long loan switch to Spanish outfit Malaga.
"The 21-year-old, who arrived at Anfield from Sevilla last summer, will spend the entirety of 2014-15 with the side that finished 11th last season."
Liverpool's hopes of signing another Sevilla player, left-back Alberto Moreno, are slim according to quotes attributed to the club's sporting director.
Spanish newspaper El Correo de Andalucia quoted Monchi as saying: "The matter of Alberto is practically settled. We couldn't reach an agreement and I don't think it can be revived.
"I don't think we'll make a lot of moves but if on August 14 a club comes along and they give you a mountain of cash, well....I know you don't like to hear it, but we are economic managers.
"My feeling is that the negotiations are paralysed and I don't see any hint that they will be restarted. We put a price on our players which we believe to be appropriate. Whoever wants to buy, can buy, and if you can't...."