Speaking to Radoyspor Kaynar said: “A loan deal is likely, it could go ahead within the next two days.”
NTV Spor reported that the Black Eagles have made a loan bid for Leiva despite initially wanting the experienced midfielder on a permanent transfer.
The Istanbul giants were unable to match the Reds €7 million asking price according to the NTV report.
Besiktas are in need of a central midfielder following injuries to Veli Kavlak and Tolgay Arslan which have ruled them out until the end of the season.
The Black Eagles were closely linked with a move for Gokhan Inler but lost out in the race to sign the Switzerland international.
Inler joined Leicester City instead, the Premier League outfit confirmed the transfer today.
Besiktas won their opening game of the season 5-2 against Mersin thanks to a hat-trick from Cenk Tosun.
The Black Eagles strengthened over the transfer window signing the likes of Mario Gomez, Ricardo Quaresma and Andreas Beck.