Everton have discussed terms of an approach worth £30million and West Ham are considering whether to match their offer for the 20-year-old.
The active contact from Everton and West Ham has left Boehly and Chelsea manager Thomas Tuchel under pressure to decide their plan for the Albania international, who is ambitious to kick on after a successful loan spell at Southampton last season.
Everton manager Frank Lampard sees Broja as a top summer target and West Ham also hold serious interest, although they continue to weigh up other potential striking options.
Meanwhile, Newcastle have seen a loan approach turned down, with Broja either looking for a substantial role at Chelsea or a permanent move to a Premier League rival this summer.
Tuchel wanted to train with most of his loanees from last year in pre-season before deciding their futures. Few players have been allowed to seek exits yet, with the manager yet to show his hand.
Still, Boehly has met with almost every single representative or agent of his senior Chelsea players. Those talks offered little clarity on whether players will get their chances in the first team, be sold or go out on loan.
Even Conor Gallagher, who won Crystal Palace’s Player of the Season award and became a full international with England last season, is waiting to hear what Tuchel will do with him next season.
Like Broja, the 22-year-old midfielder has interest from a host of clubs over a summer move with Everton also keen on bringing him to Goodison Park.
Much depends on a complicated set of negotiations across the board on new contracts for senior players, new signings and possible player sales.
Hakim Ziyech remains in talks with AC Milan over a loan deal, with the Italian champions asking for Chelsea to subsidise his wages. Timo Werner and Jorginho were also offered in a swap deal for Juventus’s Matthijs de Ligt, which was turned down.
The negotiations around Manchester City’s left-sided defender Nathan Ake could force out star academy graduate Levi Colwill, who has interest from Leicester, Southampton, Brighton and Crystal Palace after his loan spell at Huddersfield.
Left wing-back Ian Maatsen has turned down a loan offer from Dutch giants Feyenoord, favouring a move in England should Chelsea let him go.
A host of fringe players like Dujon Sterling, Malang Sarr, Ross Barkley and Timo Anjorin are training with the first team already, with Emerson Palmieri, Ethan Ampadu, Billy Gilmour, Baba Rahman, Tiemoue Bakayoko and Michy Batshuayi to join up by Saturday for the tour of the United States.