The 20-year-old forward enjoyed a successful on-loan season at Southampton last term, as he scored nine goals in 38 appearances across all competitions.
Broja impressed with his all-round play and could be the ideal centre-forward the Hammers are chasing for next season, with the east London club desperate to strengthen their attacking options next term.
According to transfer expert Gianluca Di Marzio, Broja is West Ham United's first-choice striker in the transfer market this summer and are considering a permanent deal, with a fee potentially around £25-30 million.
The agreement is not close to being agreed, although Sky Sports have reported that Southampton are also interested in bringing the Albanian international to the South Coast on a permanent deal.
Born in England, Broaja joined Chelsea's youth academy from Tottenham as an eight-year-old in 2009 and signed a new five-year-contract at Stamford Bridge last summer.
The forward has made a single appearance for the Blues when he came on as a substitute in February 2020, before heading out on loan to Dutch side Vitesse the following season.
Chelsea confident they can sign Manchester City superstar Raheem Sterling
Following a turbulent season for the Blues, the takeover by Todd Boehly should bring a semblence of security to the club, although they do need to start bringing in some players.
Having lost both domestic cup finals and finished well short of the Premier League's top two, the club clearly feel that they need to bring in a statement signing.
The reported £30 million the west London outfit may bring in for Broja could go towards capturing Manchester City forward Raheem Sterling, who has been consistently linked with a move to the two-time European champions.
Sky Sports have claimed that Chelsea are confident of bringing the England international into the club, with Thomas Tuchel a huge admirer of the 27-year-old.
However, City are understood to value Sterling at £60 million, despite him only having one year left on his current contract.
The former Liverpool winger scored 17 times and provided nine assists in his 47 appearanes for Pep Guardiola's side last season, although he was regularly left out of the club's biggest encounters across the campaign.
Chelsea will be aiming for a squad rebuild this summer under Tuchel and Sterling could become a centrepiece of the German's team if he were to make the move to a Premier League rival.