Everton are in discussions with a United States-led consortium about a potential £200m takeover.
The group, led by former owner of the San Diego Padres baseball team John Jay Moores and fellow entrepreneur Charles Noell, have been in talks with Toffees owner Bill Kenwright in recent months.
Moores and Noell have previously been interested in investing in Swansea.
The consortium is expected to perform due diligence on Everton's accounts over the next few weeks.
The Toffees have declined to comment on the latest interest - but there have been several parties pondering a deal to buy the Premier League club this year.
In October, City of London sources revealed to BBC Sport that American investors, some with links to Major League Soccer side Sporting Kansas City, were exploring the purchase of Everton.
The Times reports that the group led by Moores and Noell has been granted a period of exclusivity by Kenwright, which expires at the end of January, when they can examine Everton's finances.
Everton owner Kenwright has conducted a search for investment stretching back more than a decade but the latest moves are felt by those close to the club as representing the most positive and hopeful development since the theatre impresario indicated his willingness to sell.
Kenwright, who bought the club from Peter Johnson for £20m on 26 December, 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."
And former Everton midfield man Peter Reid told BBC Radio 5 Live on Wednesday: "It's my club and Goodison Park - as much as I love it - I think Everton need a new football ground.
"We've got a great squad of players and a good manager but we need to get a new stadium to keep pace with the other clubs in this Premier League. You need the revenue that generates. If Bill Kenwright says it's OK - yes let's get it done."
It is understood that after years of inactivity regarding a sale, there has been a growing intensity and intent to do a deal in recent months, fuelled by growing, serious interest from a number of groups.
If the deal is completed it would mean both Merseyside Premier League clubs would be under American stewardship. Moores, who bought the San Diego Padres from current Liverpool chairman Tom Werner for $80m (£53.7m) in 1994, is believed to be worth around £500m.
Moores and Noell have background in technology. Moores founded BMC software and also JMI Equity, a venture capitalism arm of his empire, which Noell helped to co-found.