The deal could include shirt sponsorship and a possible rebrand of The City Ground.
The report claims that Football League approval is one hurdle currently holding up the deal, which would see Forest secure what is described as a 'significant investment' from Greek shipping magnate Evangelos Marinakis.
According to the Post, Marinakis, owner of Super League champions Olympiakos, would acquire a majority stake in the Championship club, with current owner and chairman Fawaz Al-Hasawi staying on in the latter role.
It is claimed the takeover could include possible sponsorship from Marinakis and even see Forest's City Ground home rebranded.
Marinakis' interest in Forest was first reported at the end of March while Al-Hasawi posted a picture on Instagram the following month, which appeared to show him on holiday in Athens - close to Olympiakos' Piraeus base.
Forest finished 16th in the Championship this season, but recently had their 18-month-long transfer embargo lifted.
Should Marinakis' investment materialise, it would come as a timely boost for the Reds and in search for a new manager and players ahead of next term.