The latest reports follow La Liga giants Atletico Madrid being linked with a £17 million move for the Bundesliga star.
Per the source, the German giants would only accept a bid of £21.4 million or more which would make a considerable increase on the £12.5 million they invested in him back in 2014 when he joined from HSV.
In a recent interview with the BILD, Calhanoglu could not rule out leaving Bayer over the summer transfer window.
When asked if he will stay at Bayer Leverkusen, Calhanoglu responded by saying: “You never know in football what will happen.”
The Turkish international attacking midfielder does have another three-years remaining on his contract and Bayer will only accept an offer than matches their valuation.
The 22-year-old is widely regarded as one of the best free-kick takers in the world and has already scored 11 times from direct set-pieces in the Bundesliga.