Matthews has reportedly gone into quarantine at his home in Arizona.
Several unidentified Arizona Coyotes players who were training alongside Matthews recently tested positive, according to Simmons, whose sources also indicated Maple Leafs goaltender Frederik Andersen did not test positive.
Andersen had been spending time with Matthews during the pause, but is no longer living with him and isn't in the state anymore.
The team neither confirmed nor denied the report in a statement issued Friday evening.
"Per the National Hockey League protocol with respect to COVID-19, the Toronto Maple Leafs will not be commenting on reports surrounding testing for any of the club's players or staff," the team said, according to Sportsnet's Chris Johnston.
"A person's medical information in this regard is private. The club will defer to the NHL's policy on handling the disclosure of positive test results, in that the league will provide updates on a regular basis with aggregate totals of the number of tests conducted and number of positive tests reported without disclosing either the identities of affected clubs or players."
Arizona has been a hotspot for COVID-19. The state has recorded a new single-day record of 3,246 cases since Thursday, when it set its previous high mark with 2,519 cases, according to the Arizona Department of Health Services.
The Tampa Bay Lightning shut down their training facilities earlier Friday after three unnamed players and multiple staff members tested positive.
Unnamed players on the Ottawa Senators, Colorado Avalanche, and Pittsburgh Penguins have also been confirmed to have contracted the coronavirus since March.