The report claims that the Brazilian midfielder will join Beşiktaş on loan until the end of the season.
Leiva is expected to undergo a medical after arriving in Turkey before putting pen-to-paper on a new deal.
In a conflicting report the Liverpool Echo reported that the Reds rejected the loan-bid from Beşiktaş for Leiva.
The report claims that the Reds have recalled Leiva to the team following injury to captain Jordan Henderson.
The Brazilian midfielder will be given another chance to fight for his place in the Liverpool team.
The Black Eagles have also been linked with Chelsea midfielder Mikel as they continue efforts to strengthen in midfield following injuries to Veli Kavlak and Tolgay Arslan.