The billionaire has been backed to add Italian side AC Monza to his club portfolio following the death of their owner Silvio Berlusconi last year.
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Marinakis is said to want the Italian side who finished 12th in the Serie A and could purchase them this season.
The businessman also owns Europa Conference League champions Olympiacos in his homeland of Greece as well as Portuguese side Rio Ave.
If the purchase does happen then Forest could have the opportunity for loan moves which have already happened previously with Olympiacos in past seasons.
Rumours about the takeover have existed for a year now and if a move is not made soon the current owners of the club, the Berlusconi family could look elsewhere for a buyer.