"I asked him flat out, 'Do we have any (issues)?'" Babcock said Friday. "He was sitting right there. We don't seem to."
Matthews seemed irked by a Sportsnet report following a Game 7 loss to the Boston Bruins that he and Babcock were at odds.
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"I don't know what that's all about," he said. "Our relationship's fine. Obviously, you guys can speculate all you want, but I think it's pointless.
"Stuff happens, people speculate. I can tell you right now it's not the case."
Babcock and Matthews discussed the issue during an end-of-season meeting Friday. Babcock on Thursday received a text from a friend referring to a report suggesting the strained relationship with Matthews.
"I said, 'What's going on?'" Babcock said. "It's interesting, in Toronto, you (media) do such a good job. You're everywhere. You're under the bench, you're in the crack in the door, you're in the car, you're in the parking lot. You're everywhere, and anytime anybody does anything, there's a big story."
Sportsnet analyst Nick Kypreos on Thursday said Babcock had lost Matthews for various reasons, and that the 20-year-old has trust issues with his coach.