As a result, and after a slow start at training camp, the veteran center was sent down to the Leafs' AHL affiliate, the Toronto Marlies, making room for Nazem Kadri and Matt Frattin.
In 12 games, 31-year-old Connolly has recorded five goals and two assists for seven points with the Marlies.
Nonis, however, doesn't expect Connolly to spend the rest of the season in the AHL.
"Is there a chance [Connolly] will be back [in the NHL]? No question," Nonis told Sportsnet 590. "We've had teams call on him. I would expect at some point, whether it's with us or someone else, that he'll be back in the NHL before the season's over."
Connolly is in the last year of his contract, which pays him $4.75 million a season, and will become an unrestricted free agent at the end of the season.