Manager Maurizio Sarri has yet to be convinced by Alvaro Morata or Olivier Giroud and has been impressed by Mitrovic's form, according to the Mirror's John Richardson.
The 24-year-old has four goals in five games for the Cottagers this season, but manager Slavisa Jokanovic will want to do everything he can to keep hold of the Serbia international.
Sarri prefers to play with one striker and has Morata and Giroud to choose from after allowing Michy Batshuayi and Tammy Abraham to leave on loan.
However, the Spain international endured a difficult first season at Stamford Bridge. He lost his place in the team to Giroud, and he also was left out of Spain's squad for the 2018 FIFA World Cup.
Morata has said he thought about leaving the club, per ESPN UK:
He has made four appearances for Chelsea this season, scoring once in the 3-2 win over Arsenal. However, doubts remain over whether he can be a success for Chelsea.
Giroud is a proven Premier League striker but will turn 32 on September 30 and is heading towards the end of his career.
The Guardian's Jacob Steinberg doubts whether either can win the title for Chelsea:
Chelsea may decide to strengthen their attack, and Mitrovic is one of the English top flight's in-form strikers.
Mitrovic is known as being a fiery character, but he's also a powerful and dynamic striker. Scouted Football noted how he's in a rich vein of form for club and country:
The youngster still has some way to go before he can prove he can be a consistent goalscorer in the Premier League. If he can maintain his early-season form, he is bound to attract interest from bigger clubs.