The Turkish giants sold the 21-year-old to the Scottish giants in the summer, but he has taken his time to adapt to Scottish football, with playing time limited.
He is currently sidelined with a hamstring injury and is not expected to return to action until December.
Besiktas have kept a close eye on how Yilmaz has fared in Scotland and new Black Eagles coach Gunes feels the time is right to bring him back.
The 70-year-old wants to strengthen his squad in January and is keen to land Yilmaz, according to Turkish outlet En Son Haber.
It is claimed that Besiktas will test Rangers by looking to sign Yilmaz on loan for the second half of the season.
It is unclear how Rangers might respond to a loan proposal from Besiktas.
The opportunity to play regular football back in Turkey might appeal to Yilmaz, but whether Rangers would agree remains to be seen.
