Antonio Conte is keen to bolster his frontline and bring in support for Alvaro Morata.
Having told Diego Costa he has no future at Stamford Bridge, Chelsea need another goalscorer.
Starsport understands Torino star Andrea Belotti is of interest to the Premier League champions.
But Leicester hitman Vardy has also been linked with a surprise move to west London.
The 30-year-old turned down a move to Arsenal last summer.
But according to The Mirror, Chelsea are making a £40m move to land the England international before Thursday’s deadline.
Vardy earns £100,000 a week at the King Power Stadium, but knows the Blues would bolster his salary.
Chelsea apparently believe he is open to a new challenge.
But they face competition from Everton as Ronald Koeman eyes a proven striker to complete his summer spending.
The Mirror add the Toffees are set to bid for Vardy as they look to usurp Chelsea in the race for his signature.
Everton have the advantage of having former Leicester chief scout Steve Walsh as their director of football.
And Koeman’s side would also be willing to up his wages as they bid to effectively replace Romelu Lukaku.
Everton have also asked Chelsea about taking Costa on loan.
And that prospect may be discussed when the two sides go head-to-head tomorrow at Stamford Bridge (1.30pm).
