The BBC say that the American - who is worth almost five billion dollars - has now decisively moved ahead of other potential bidders for Everton.
Friedkin also owns AS Roma in Italy's Serie A, and now apparently has moved closer to securing control of his first Premier League club.
As a result, he is it seems about to enter into an exclusivity agreement with Moshiri, the fourth such agreement that Moshiri has entered since he first tried to sell the Toffees.
Everton's current owner certainly has not got a great track record in this respect, something that has been bourne out again with the saga over 777 Partners bid that finally failed at the end of May.
That situation had become untenable as the Miami-based investment group - who agreed to buy the Blues from Moshiri in September - became increasingly mired in various financial issues and with more and more questions about their ability to complete a takeover.
All this came too at the end of what had been the most challenging, chaotic and controversial season that any Premier League club has gone through.
And so while there may be hope with this news that things could be moving in a positive direction as far as resolving the club's ownership is concerned, there will be plenty of misgivings too.
So once again, who exactly is the latest American tycoon trying to acquire Everton Football Club?
Friedkin is a Texas-based businessman who has a background in the automotive trade specifically selling Toyota's to the US market. He is also involved in the movie business as well.
At least too he has experience running a historically big club with a huge fan-base and one that aspires to return to past glories, however tenuous that may seem in Everton's case at the moment.
As to whether any of this still makes him a better bet than others who have allegedly expressed interest in the Blues, is an open question.
Just recently too his current football club were linked to Everton as stories emerged that the Toffees were again interested in Roma's English striker Tammy Abraham.
Anyway it seems as though we go again with another takeover process apparently about to begin, if media reports are to be believed.
Will this one finally turn out to be for real and will it mean at last a change in fortunes for this great club? For one thing it would be good to see an Everton owner holding a piece of silverware for a change!