According to The Sun, the Blues have made a transfer offer of Olivier Giroud plus cash for Lyon striker Moussa Dembele.
The french man has fallen down the pecking order at Chelsea and he is expected to leave the club this January.
According to Sky Sports, Chelsea boss Frank Lampard sees similarities between Dembele and Chelsea legend Didier Drogba, who was also his teammate at Chelsea.
Dembele has notched 10 goals in 18 Ligue 1 matches this season but failed to score in the Champions League.
Chelsea will reportedly face competition from Arsenal for the Frenchman.