Sky News has learnt that Fenway Sports Group (FSG), the Anfield club's controlling shareholder since 2010, is preparing to make an announcement about a transaction as soon as this week.
The deal will see Mr Bezos participate in an investor group alongside Eduardo Saverin, one of the co-founders of the social network Facebook.
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The syndicate is led by Amit Bhatia, the son-in-law of steel billionaire Lakshmi Mittal and until recently a shareholder in Championship club Queens Park Rangers.
One source indicated that an announcement was expected in the coming days, although they cautioned that it could slip into next week.
If completed, the deal would install a trio of the world's wealthiest individuals as co-owners of the Reds, one of the most successful teams in the history of English football.
Mr Bezos alone has a fortune estimated by Forbes at over £207bn ($280bn), while Mr Saverin is said to be worth over £23.7bn ($32bn).
Their investment in Liverpool will reportedly value the club at £4.4bn ($6bn), making it one of the sport's richest-ever deals.
Sky Sports News has contacted Liverpool and FSG for comment.
While Mr Bezos has not previously been linked to deals in football, his prospective involvement in the Liverpool FC consortium underlines the extent to which sport is now viewed by wealthy investors as an asset class in its own right.
Mr Saverin, who is 44 years old, was part of a consortium which assembled an unsuccessful takeover bid for Chelsea FC during the 2022 auction triggered by Vladimir Putin's invasion of Ukraine.
One insider said the deal was now expected to be slightly larger than previously thought, potentially involving a stake of over 30 per cent.
Nevertheless, if its valuation hits £4.4bn ($6bn), the deal will reinforce the huge financial success that FSG has enjoyed during its 16 years as the club's owner.
The Boston Red Sox owner acquired Liverpool for just £300m with the club in a troubled state financially.
The arrival of such a powerful consortium will fuel expectations that its members will ultimately seek outright control of the Reds.
A spokesperson for FSG said last month: "An investment consortium led, managed, and represented by Amit Bhatia has expressed interest in making a strategic minority investment in Liverpool Football Club."
FSG declined to comment further on the potential timing of a deal.
A spokesman for the consortium led by Mr Bhatia also declined to comment.
The last time a stake in Liverpool changed hands was in 2023, when Dynasty Equity bought a small interest valuing it at more than £3.3bn ($4.5bn).
