The report claims that the Reds have recalled Leiva to the team following injury to captain Jordan Henderson.
Leiva will be given another chance to fight for his place in the Liverpool team.
The experienced midfielder has been linked with a move abroad and Beşiktaş are reported to be in talks over a loan move according to football agent Ahmet Bulut.
“The player is keen on a move to Turkey, in my opinion the move is close to completion,” Bulut told Radyospor.
Leiva has struggled for playing time after a series of injuries but has failed to regain his place in the team after recovering.
The experienced midfielder has yet to start for Liverpool this season.
The Reds take on Arsenal at the Emirates stadium on Monday 24 August in the Premier League.
Liverpool have won their two opening game of the season against Stoke City and Bouremouth.