According to the Mirror, incoming Pensioners boss Antonio Conte has targeted the Belgian forward who he sees as a big part of his summer rebuild at Stamford Bridge.
The Blues are set to face competition from one of their Premier League rivals, with Manchester United also understood to be keen on signing the powerful attacker this summer.
However, the tabloid note that the west London side are confident off seeing off the Red Devils to the signing of the former West Bromwich Albion attacker.
Should he sign for Chelsea, it would be Lukaku’s second stint at the club, having originally moved to Stamford Bridge in 2011.
He remained on the Blues’ books for three years, but managed only 10 Premier League outings without scoring a goal, before being sent away on loan to the Albion and then Everton.
Now 23, Lukaku has impressed this term, scoring 18 goals and contributing six assists in 37 appearances.