City of London financial sources have told BBC Sport that American investors, with links to Major League Soccer side Sporting Kansas City, are exploring purchasing the Premier League club.
An asking price of £225m is believed to have been set by Everton's owners although it is unknown if the US consortium are prepared to match that.
The possible deal has also been reported in Kansas City.
SKC representative Mike Illig has publicly stated he is an Everton fan, posting pictures of a visit to Goodison Park on his Twitter account on Thursday.
Illig attended former Everton striker Duncan Ferguson's testimonial against Villarreal at Goodison Park in August. His picture of the stadium was retweeted by Robb Heineman, Sporting Kansas City's CEO, increasing speculation that a deal is under discussion.
Cliff Illig, Mike's father, is the principal investor in the group of Kansas City entrepreneurs that purchased Kansas City Wizards from the Hunt Sports Group in 2006. He is also co-founder of the Cerner Corporation health care information technology group.
Everton chairman Bill Kenwright has openly admitted the club is for sale and has been seeking investment but failed to attract a buyer.
The theatre impresario, who bought the club from former owner Peter Johnson for £20m on Boxing Day 1999, said as far back as November 2007: "If the right person stands in front of me and wants to take this club forward then I will sell."
Everton did not comment when contacted about suggestions that a takeover deal is under discussion.
Everton are the subject of renewed speculation over a potential takeover.