The 30-year-old Dutch midfielder started his career in Ajax's famous youth system and had spells with Bordeaux, Malaga, Atletico Madrid and Trabzonspor as well as Manchester City for whom he played 41 games between 2004-06.
Musampa, who was released by Dutch club AZ Alkmaar on January 1, is a free agent and was initially linked with a move to either Korea or Japan.
Yet he has begun a one-week trial with Toronto at their pre-season camp in Bradenton, Florida.
The Canadian side recorded a first victory under incoming coach Carver on Saturday with a pre-season 2-0 win over the Kansas City Wizards.
Toronto play again on Sunday with a friendly against the United States under-17 side.
Former Sunderland midfielder Carl Robinson will leave the training camp Sunday to return to Wales to be with his wife, who is expected to give birth next week.