It sounds, at least based on speculation, that the Leafs have interest in bringing back one unrestricted free agent:
The club’s top goal-scorer last season, P.A. Parenteau, is set to become an unrestricted free agent on July 1, and he may be the only impending UFA Toronto seriously considers re-signing........
"There have been a couple of discussions. Very preliminary. I would say every possibility is on the table," Partenteau's agent, Allan Walsh, told Sportsnet. "They have not closed the door to him coming back, but I don't think it's a decision that's going to be made now. I think it's a decision that's going to be made just before we get to July 1."
First, some obvious qualifications here. This is nothing yet but basic speculation and "talking," so evaluate it for what it's worth. Further, recall that the Leafs are currently the only team that can have contract discussions with Parenteau until the free agency contacting period begins on June 25. It would be quite easy for the Leafs to make progress on contract negotiations with a player whom only they may negotiate.
That said, re-signing Parenteau would be a good move for the right value. After a couple seasons struggling under Patrick Roy in Colorado and Michel Therrien in Montreal, Parenteau succeeded under Babcock, scoring 20 goals and 41 points in 77 games. It was his best offensive season since scoring 43 points in the lockout-shortened 2012-13 season with the Colorado Avalanche. It was also only the second season in which Parenteau scored 20 goals, the other time being with the New York Islanders in 2010-11. The difference? Back then, he played on John Tavares' wing; in 2016, he was paired with Tyler Bozak.
The other point in favour of re-signing Parenteau is the Leafs' depth chart at right wing, which is.....well, not very good. Even with one of William Nylander or Mitch Marner (most likely the latter) being shifted from centre to the wing, the Leafs only other signed players at that position are Leo Komarov, and....that's it. The 33-year old might be a useful piece to round out the depth chart.
The only reservation in bringing Parenteau back would be money and term. The Leafs signed him in 2015 to a one-year, $1.5 million "show me" deal after a couple of bad seasons. Well, he did show them, and he'll probably want a contract with a higher AAV and at least a couple years of term. The Leafs will need to determine if his contract expectations jive with their long-term plans.