Amuzu, who can play on either flank, is used predominantly as a substitute by the Brussels-based club and according to media in his homeland, Rangers manager Giovanni van Bronckhorst is keen on the 22-year-old.
L’Avenir claims that the defending cinch Premiership champions are monitoring his situation, although English Premier League outfit Everton and German Bundesliga side Wolfsburg are also interested.
Van Bronckhorst recently deployed scouts to Belgium and appointed Zeb Jacobs to their backroom team, who knows the market well in his homeland.
Amuzu has come through the ranks at Anderlecht, making 129 appearances for the club and scoring 11 goals. He has also notched up 15 assists.
Rangers dipped into the Jupiler League last summer by signing Fashion Sakala for Oostende and Van Bronckhorst is keen to bring in his own players and replenish his squad for the second half of the season.
Current winger Ryan Kent has also been lined with a winter move to Aston Villa, which would see him join up with former manager Steven Gerrard.