The 23-year-old Spaniard has not played for the Reds since January 2014 but has impressed during loan spells back in his home country.
There has been much speculation about which members of Liverpool's squad Jurgen Klopp will be looking to sell this summer, and according to the Liverpool Echo one of such player is a man who has been pretty much forgotten at Anfield, midfielder Luis Alberto.
The 23-year-old Spaniard joined the Reds for £6.8 million from Sevilla three years ago but has failed to set English football alight.
Alberto played 12 times for the Merseyside club during his first half-season in England, but his last appearance for the club came in January 2014 as he quickly fell out of favour.
He spent a relatively successful spell on loan at Malaga in 2014-15, and last season he starred for Deportivo La Coruna in La Liga, scoring six goals in 29 league appearances.
The midfielder has returned to Melwood for pre-season training but Liverpool are not thought to have any real interest in reintegrating him into the side, and they will listen to offers this summer.
The Echo reports that several Spanish clubs are interested in bringing the playmaker back to La Liga permanently, including his former club and Liverpool's Europa League conquerors Sevilla.
However, the paper claims that the Reds believe Alberto's impressive displays during his loan stints have only seen his stock rise, and they are willing to hold out to at least recoup the entirety of the fee they paid for him in 2013.
Sevilla are thought to be preparing a bid this week, but although the player would likely be keen to make the switch, Liverpool will hold firm until they feel an offer is suitably high enough to accept.