The Hammers have managed to bring in Nayef Aguerd, Alphonse Areola and Flynn Downes on permanent deals already this summer.
Manager David Moyes had stated he wanted to bring in as many as six new faces into the dressing room, with centre-forward, left-back and central midfield the remaining positions targeted for strengthening.
Lille rejected two bids from the Hammers for Belgian defensive midfielder Amadou Onana and they are evaluating whether to go in with an improved third bid or move on to other targets.
Broja is their primary target to spearhead the attack, but in the event a permanent transfer cannot be agreed with Chelsea, the Hammers have other unnamed high-profile targets lined up.
While on loan at Southampton during the 2021/22 season, Broja made 38 appearances in all competitions, scoring nine goals and laying on an assist.
Chelsea have yet to make a decision on the future of the Albania international, though he has not joined up with the rest of the squad currently in the US for their pre-season tour.
West Ham United managed to qualify for European competition for the second season running under Moyes’ stewardship after finishing last season in seventh place.
