Everton have reportedly entered an exclusivity agreement with MSP Sports Capital over potential investment.
Farhad Moshiri, who owns a 94% stake in the Toffees, revealed in January that he was looking to bring investment into the Merseyside club.
Speaking at Everton's Fan Advisory Board, Moshiri said: "The club is not for sale but I've been talking to top investors, real quality, to bridge a gap on the stadium finance.
"I can do it (finance the new stadium) myself but the reason I want to do it is to bring top sport investors into Everton - for some of the reasons the fans want: improvement, more talent."
MSP Sports Capital and 777 Partners are among the companies that have been in the running for a minority investment in the Toffees.
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According to BBC Sport, New York-based firm MSP Sports Capital have now moved ahead of 777 Partners after they entered an exclusivity agreement for investment in the club.
The report claims that talks over funding are progressing, but there is still work to be done before a deal can be completed.
MSP already have stakes in Bundesliga outfit Augsburg, Estoril of Portugal, Brondby in Denmark and Spanish third-tier side Alcorcon.
Their chairman, Jahm Najafi, is also the vice-chairman of McLaren Racing and a minority owner of the NBA franchise Phoenix Suns.
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There has been speculation that a deal could be wrapped up before the end of the week, but any potential deal is unlikely to be agreed until Everton's Premier League fate is decided.
Sitting just outside the relegation zone in 17th position, Everton are currently at risk of being relegated from the top flight for the first since 1951.
Leicester City's goalless away draw with Newcastle United ensures that the Toffees head into the final weekend of the season with their destiny in their own hands.
Sean Dyche's side are two points clear of Leicester City and Leeds United, who occupy 18th and 19th position respectively.
Should the final day go down to goal difference, the Toffees would have the advantage over Leeds, but they are six goals worse off than Leicester.