The group, led by former owner of the San Diego Padres baseball team John Jay Moores and Charles Noell, are believed to have been in talks with Toffees owner and Chairman Bill Kenwright.
The deal is believed to be in advanced stages and estimated to be worth £200million.
A positive development in the club's search for investment
The Times Newspaper reports that the group - led by Moores and Noell - has been granted a period of exclusivity by Kenwright to examine the club's finances over the next six weeks.
Everton owner Bill Kenwright, who bought the club from Peter Johnson for £20million in December 1999, has been searching for new investment for nearly a decade, but he has yet to find the right party to sell to.
There has been a growing interest in buying the club from a number of groups. In October, American investors with a link to Major League Soccer side Sporting Kansas City were reported to have been exploring the purchase of the club.
However, Kenwright has always maintained that he will only sell to the right person and, after years of inactivity regarding a sale, this latest move represents a positive development in the club's search for new investment.
Who are Moores and Noell?
If the deal were to go through, it would not be Moores' first investment in sports as he is the former owner of Major League Baseball outfit San Diego Padres, purchasing the franchise from current Liverpool chairman Tom Werner.
He and Noell were also in talks to buy a stake in Swansea City, but the deal did not go through because of doubts among supporters regarding foreign investment.
Moores, who is believed to be worth in excess of £500million, made his riches from BMC Software, which has become one of the largest software firms in the United States.
Noell first became involved with Moores 1992, when he set-up JMI Equity - a firm which invests in software and healthcare IT companies - Moores provided funding for the venture.
Another Premier League club with American owners?
Everton could become the second Premier League club side to get American investors in less than two months, if the deal were to go through, after Crystal Palace agreed to sell a stake of their club to Joshua Harris and David Blitzer.
It would also mean that both Merseyside Premier League clubs would have American owners, with John W. Henry owning Liverpool.
They could join an ever-growing list of Premier League clubs with American investment with Arsenal, Aston Villa, Manchester United and Sunderland all owned by Americans along with Crystal Palace and Liverpool.