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.