Clement has emerged as the clear favourite to take over at the Ibrox-based club with talks now centring over personal terms and the playing budget.
The 49-year-old is highly rated within European football and was picked out by Monaco to take charge following an impressive spell at Club Brugge.
He has been going up against Muscat, but in the eyes of the Rangers board, his experience in Europe has given him the edge.
Muscat, who has managed in Australia and Belgium and is currently the manager of Japanese side Yokohama F. Marino, is a less experienced manager in Europe than Clement.
Clement has had two meetings with the Rangers hierarchy, the first of which was with their interview team and the second with chairman John Bennett.
It now remains to be seen how long Rangers wait until confirming Clement as their new man-in-charge.
The Belgian will want to make sure he has enough of a budget to go toe-to-toe with Celtic in the Scottish Premiership.
