The Blues confirmed last week that they have reached an agreement with a consortium led by Boehly, who is also the part-owner of baseball side LA Dodgers.
Neither of those bodies are expected to block the bid, and the Evening Standard reports that Boehly's top priority when he arrives at Stamford Bridge will be to kickstart the club's summer transfer plans.
Chelsea have been under a transfer embargo since soon-to-be former owner Roman Abramovich was sanctioned by the government for his close ties to Russian president Vladimir Putin following Russia's invasion of Ukraine.
The uncertainty surrounding the club's immediate future had impacted their transfer plans, while also preventing them from agreeing new contracts with the players due to become free agents this summer.
Antonio Rudiger and Andreas Christensen are both expected to leave West London at the end of the season, while there has also been growing speculation over the futures of captain Cesar Azpilicueta and full-back Marcos Alonso, both of whom have been linked with Barcelona.
Romelu Lukaku's place in the team has also been the subject of debate, with the Belgian striker having fallen out of favour with manager Thomas Tuchel less than a year after returning for a club-record £97.5m fee.
Lukaku has reportedly turned down moves to AC Milan and Newcastle United, while his likely price tag and wage demands are understood to have priced a number of clubs out of the running for his signature.
Tuchel is open to keeping the 28-year-old at Stamford Bridge this summer, but the German manager is keen to significantly strengthen elsewhere.
Top of his priority list is likely to be defence due to the imminent departures in that area of the field, and the report claims that he wants two centre-backs in addition to greater cover at wing-back.
Tuchel has also placed an attacking reinforcement on his list of targets, while he could dip into the midfield market too, should any of his current options leave this summer.
James, meanwhile, is thought to be high on Real Madrid's list of defensive targets, although Los Blancos are expected to commit most of their transfer funds this summer to attacking talent such as Kylian Mbappe.
Boehly is expected to back Tuchel in his first transfer window as owner, with the consortium guaranteeing £1.75bn of investment into the future success of the team on top of the £2.5bn it will take to buy the club.
A chunk of that money will be made available to Tuchel, although that sum also includes funds to redevelop Stamford Bridge as well as investing in the academy and women's teams - the latter of which won their third successive Women's Super League title at the weekend.
Boehly and Walter have a track record of investing heavily in the playing staff at the LA Dodgers, spending more than £240m a year on wages including signing right-fielder Mookie Betts to a record £227m, 12-year deal in 2020. body check tags ::