Boehly is reported to have fallen short of Abramovich's £3 billion valuation of the West London club.
Boehly is the chairman and chief executive of the Connecticut based private investment firm Eldridge Industries
He is also the former president of Guggenheim Partners, a wealthy asset manager group.
This wouldn't be Boelhy's first foray into club ownership in sport as he is the co-owner of the Los Angeles Dodgers baseball team.
The 46-year-old first emerged as a possible buyer in the summer when he expressed an interest in both Chelsea and Tottenham Hotspur.
It was the uncertainty surrounding Abramovich's future that is reported to have pushed Boehly toward the Blues.
Abramovich bought Chelsea in 2003 and sparked a new era for football as cash injections began being pumped into the game.
The Russian oligarch enjoyed a spell of dominance before the likes of Manchester City upset the apple cart.
Now, however, Abramovich is in a form of exile after his application for a UK investor visa was rejected by the authorities.
The 53-year-old was granted Israeli citizenship last year and has been living out of the country ever since.
Abramovich finds himself on the FBI's 'Putin List' which names 210 oligarchs and politicians that have close ties to the Kremlin.
Whether he will, in fact, sell Chelsea is unclear, but Boehly is reportedly open to reevaluating his offer.
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