talkSPORT understands Nigeria international Osimhen is on the Blues' list of potential targets to replace Romelu Lukaku.
The Italian side are among a host of clubs tracking academy product Broja after his breakthrough season on loan at Southampton.
With Napoli valuing Osimhen, 23, in excess of £80m, a swap deal involving Broja would help Chelsea's new owner Todd Boehly reduce the financial outlay if they decide to follow up their interest.
Broja's future remains in the balance with manager Thomas Tuchel originally planning to take a good look at the Albania international during pre-season.
The 20-year-old is understood to be growing impatient with Everton, Newcastle and West Ham all in the race to sign him.
CHELSEA JOIN CHASE FOR LEWANDOWSKI
New Chelsea chief Boehly's eagerness to make a statement star signing has also seen the Blues make contact with representatives of Robert Lewandowski.
Lewandowski is desperate to push through a move to Barcelona after telling Bayern Munich he is determined to leave this summer.
Boehly has made it clear to the prolific Pole he would be interested in bringing him to Stamford Bridge if his dream move to the Nou Camp falls through.
The American businessman remains keen on Cristiano Ronaldo but Manchester United are understandably reluctant to sell their iconic star to a Premier League rival.
TOTTENHAM TURN TO PLAYER SALES
After a busy summer of incomings, Tottenham have shifted their attention to offloading players, partly to help fund a move for Villarreal centre-back Pau Torres.
Spurs have been one of the most active clubs in the transfer window so far, recruiting Richarlison, Yves Bissouma, Ivan Perisic and Fraser Forster, while Clement Lenglet and Djed Spence are due to join from Barcelona and Middlesbrough respectively.
Those signings have left manager Antonio Conte with a bloated squad, which needs to be trimmed in order to continue the spending spree, with the £30m-rated Spain international Torres high on their wanted list.
Giovani Lo Celso and Tanguy Ndombele are two big earners the north Londoners are keen to remove from the wage bill.
Former Wolves full-back Matt Doherty has also been told he can leave while Everton target Harry Winks is unlikely to play much first-team football following the arrival of Bissouma from Brighton.
Tottenham are also willing to loan out defenders Japhet Tanganga and Joe Rodon.
SAINTS SWOOP ON MAN CITY
Southampton are hoping the impending appointment of Manchester City youth talent spotter Joe Shields will help the south coast side land their third City youngster of the summer.
Shields is set to quit the Etihad Stadium to become Saints' new head of recruitment.
After snapping up goalkeeper Gavin Bazunu and midfielder Romeo Lavia from City, Ralph Hasenhuttl's men are now ready to step up interest in striker Liam Delap.
Shields has a close bond with Delap, son of former Saints midfielder Rory, after unearthing the recent England Under-19 European championship winner as a 16-year-old.
Saints have made strengthening their forward line their main priority.