Moores, the former owner of Major League Baseball franchise the San Diego Padres, and his associate have been in negotiations since December.
The pair have undergone a six-week due diligence period looking at the club's books and speaking to major shareholders chairman Bill Kenwright, Robert Earl and Jon Woods.
Reports suggest the Americans are looking to secure a deal for £200million in the next few weeks
There has been interest from other parties but none are as far down the line.
Everton have not commented on any of the recent potential takeover speculation but at the club's AGM in November chief executive Robert Elstone said: "There has never been more people interested in investing in Everton and the chairman is confident [investment] will be secured in the near future."
At the same meeting Elstone said the club's plans to move to a new £300million home in nearby Walton Hall Park were more dependent on securing partnership funding from the city council than they were on fresh outside income
"We are not working on the new stadium on the premise that we are about to secure new investment or need new investment," he said at the time.
Source: PA