Turkish Football claim Antonio Conte has been keeping close tabs on the playmaker.
Chelsea are looking to replace Oscar – who joined Chinese Super League side Shanghai SIPG for £60m.
However, the Blues face competition for the Turkey international.
“Chelsea have made a bid for Bayer Leverkusen star Hakan Calhanoglu”
Turkish Football say Manchester United have also been monitoring the 22-year-old ace.
Calhanoglu is reportedly unlikely to leave in the January transfer window but a summer move is possible.
The attacking midfielder is said to be keen on a Premier League move in the future.
Calhanoglu still has two-and-a-half years remaining on his current contract with Leverkusen.
The Bundesliga star has been in impressive form this campaign.
He has netted five goals and chipped in with six assists in all competitions.