Per the source, the Reds want to send the U21 Spain international on loan and Fenerbahce want to bring in an attacking midfielder over the summer.
The Express however, report that Alberto is close to a cut-price move to Valencia worth £2.6 million which would be considerably less than the £6 million Liverpool invested in him back in 2013 after signing the attacking midfielder from Sevilla.
Alberto has struggled for playing time at the Premier League outfit making just nine appearances for the Reds since joining.
The 23-year-old had an impressive season on loan at Deportivo last season in the La Liga scoring six times and providing seven assists in 29 games.
Fenerbahce are currently coached by Dick Advocaat who replaced Vitor Pereira as manager last week and he wants to bring in an attacking midfielder after being left unconvinced with the current options at the club.