Dubai-based magazine Arabian Business suggests the sale has been agreed.
Fahim is a board member of the Abu Dhabi United Group that bought Manchester City last year.
“He did the Man City deal and got the taste for football. He has followed the Premier League very closely since then, and has been looking for a club to get involved in,” Arabian Business quoted a source as saying.
“Portsmouth is a great club, with great history and great potential. It’s something he is very excited about, and I am sure all the Portsmouth fans will be equally excited.”