Bezos, one of the world's richest men, could become part of the group led by British-Indian businessman Bhatia, the son-in-law of billionaire steel tycoon Lakshmi Mittal.
Sky News reported Bezos' interest but said he is not certain to proceed with the potential plan.
The 62-year-old American is estimated by Forbes to be worth around £192 billion.
Liverpool's owners Fenway Sports Group confirmed on Tuesday Bhatia's consortium had approached them to discuss buying a minority stake in the 20-time English champions.
Bezos has reportedly explored previous bids for the NFL's Seattle Seahawks and Washington Commanders, but decided against pursuing either deal.
Bhatia's interest in the Premier League club came on the same day the 46-year-old stepped down from the board at QPR.
He ended an 18-year association with the English Championship team by transferring his stake to majority owner Ruben Gnanalingam.
In 2023, FSG sold a minority stake in Liverpool to investment firm Dynasty and any deal with Bhatia, should it proceed, is expected to be along similar lines.
According to the Financial Times, a deal with the consortium led by Bhatia would value Liverpool at more than $6 billion (£4.59bn).
FSG, which also owns the Boston Red Sox baseball team, bought Liverpool in 2010 for £300 million.