Reports in Turkey last month suggested Antonio Conte is eyeing a swoop for the 23-year-old at the end of the season.
Stamford Bridge chiefs will trigger Calhanoglu’s £33.2m (€38m) release clause, according to Ajansspor.
And it’s claimed they plan to hand Calhanoglu a three-year deal.
The Turkey international’s agent Bektas Demirtas has already reportedly conducted a preliminary meeting with Chelsea.
Demirtas last week opened the door to a move away from Leverkusen for Calhanoglu.
He said: “Hakan will be [under contract] at Leverkusen for three years.
“If an offer comes along that is fine for Bayer and which also fits with Hakan, we will do a transfer. But the final decision lies with the club.”
Calhanoglu has impressed for Leverkusen since joining from Hamburg in 2014, scoring 28 goals in 114 games for the club.
He is currently serving a four-month FIFA suspension for breach of contract with Trabzonspor, who claim he agreed to join them from Karlsruhe in 2011.