The Toronto Maple Leafs coach and the 20-year-old center each denied there were problems between the two after Toronto was eliminated by the Boston Bruins in Game 7 of the Eastern Conference First Round on April 25.
Sportsnet analyst Elliotte Friedman reported it is an effort to clear the air and address any problems they may have.
"Our relationship's fine," Matthews said two days after Toronto was eliminated from the Stanley Cup Playoffs. "Obviously, you guys can speculate all you want, but I think it's pointless."
Matthews had one goal and one assist in seven games against the Bruins and played six shifts for 4:05 in the second period of the 7-4, Game 7 loss. He looked unhappy sitting on the bench in the third, when he played 8:16 and Toronto allowed four goals.
"Auston was [angry] in the third period, in the last 10 minutes of the last game," Babcock said then. "Probably 23 other guys on the team were the same."
Matthews, who had 63 points (34 goals, 29 assists) in 62 games during the regular season, missed four games because of a back injury (Nov. 8-16), six games with a concussion (Dec. 10-20), and 10 games with a shoulder injury (Feb. 24-March 20).
Babcock was questioned during the series for not having Matthews on the first power-play unit. Forwards Tyler Bozak, Mitchell Marner, William Nylander and James van Riemsdyk, and defenseman Morgan Rielly had more power-play time in the series than Matthews. Toronto was 4-for-15 in the series.
"Auston's a young man trying to be the best player in the world," Babcock said. "The hardest part in life is when you're disappointed and you thought you maybe could have done more. I know that from me as a coach ... it makes you sick, almost.
"He's a good young man. We're lucky to have him. I'm lucky to get to coach him, and we continue to grow our product here with him leading the way."
The Maple Leafs were 49-26-7 during the regular season, setting their records for wins and points (105). They were eliminated in the first round for a second straight season.