Appearing on Toucher and Rich (h/t Chris Forsberg of NBC Sports Boston), Ainge said no teams have called him about Rozier since the start of the season.
On Wednesday, Shams Charania of The Athletic and Stadium reported that at least seven teams are monitoring Rozier in hopes of acquiring him.
Charania also reported that Rozier has been unhappy with his playing time, but Ainge saidRozier hasn't mentioned anything about that to him, and added that he believes Rozier would "come to me and talk to me or [head coach] Brad [Stevens], and that hasn't happened."
Rozier has been used exclusively as a bench player this season, and he is averaging 7.5 points, 4.4 rebounds and 2.1 assists in 22.7 minutes per game.
The 24-year-old averaged 25.9 minutes per game last season and took on a greater role when point guard Kyrie Irving was out with a knee injury.
Irving missed Boston's entire playoff run, which was the catalyst for Rozier's coming-out party.
The 2015 first-round pick out of Louisville played 36.6 minutes per game over 19 playoff contests and averaged 16.5 points, 5.7 assists and 5.3 rebounds.
With Irving and Gordon Hayward back in the fold this season, Rozier is only eighth on the team in minutes played per game.
Rozier can become a restricted free agent after the season, and Boston may have a difficult time retaining him.
The Celtics already signed guard Marcus Smart to a four-year, $52 million deal during the offseason, and they will likely need to sign guard Kyrie Irving to a max contract following the 2018-19 campaign, if he opts out of his deal as expected.
Rozier showed during the playoffs that he has star potential, and while it is a luxury to have a player of his caliber on the bench, Boston may risk losing him for nothing if it doesn't trade him this season.