A report from ESPN Brazil surfaced on Thursday, quoting Barbosa as saying he tried "several times" to request a trade, but that Ainge refused because he likes Barbosa's game.
Because of Boston's depth at both guard positions, playing time has been hard to come by for Barbosa, who's averaging just 10.7 minutes per game this season and has played five or fewer minutes in four of Boston's past five games.
"I won't lie to you. I've tried to get out several times, but Danny Ainge doesn't want to let me leave," Barbosa told ESPN Brazil. "He is a guy that I've admired in basketball for many years. I was supposed to have gotten a good contract from the Boston Celtics, but it did not happen. He's not going to let me leave this way."
Barbosa was all smiles while taking shots on the the team's practice court before Thursday's afternoon session. When the Boston Herald showed Barbosa the ESPN Brazil story, he told the paper, "No, I want to play. I want to be here. That's it."
Ainge said Thursday he was unfamiliar with the ESPN Brazil report and while he has had discussions with Barbosa about his role with the team, there have been no trade demands.
"I think it's been hard for [Barbosa] not to get an opportunity to play as much as he's wanted, but we have said from the beginning, even before he signed here, that minutes might be difficult to come by, because we were deep at that position, and he still chose to come here," Ainge said. "Actually, early in the year he played more than I expected him to play, and he played pretty well. So I think that we have had a couple of conversations, just about his role and where it went and he seemed satisfied with it. But he's never demanded or asked to be traded or any of those things at all."
Barbosa, who signed with the Celtics in October, 2012, for the veteran's minimum, has shown flashes of being a dynamic scorer in some of his brief stints on the court this season. In Boston's first game of the season, he came off the bench to score 16 points in 16 minutes, nearly rallying the Celtics against the Miami Heat.
In Wednesday's 90-79 loss to the New Orleans Hornets, he put in a quick seven points in just three late fourth-quarter minutes, which prompted coach Doc Rivers to admit after the game that he should have used Barbosa earlier.
Ainge said Thursday he still expects Barbosa to fill a greater role for the Celtics in the future.
"I think his chance will come. I think that he'll get an opportunity to play more significant minutes and in those minutes get an opportunity to earn more," Ainge said. "He's played well in practice. He's played every opportunity he's gotten. The game where [Rajon] Rondo didn't play in New Jersey, I thought he started at the point guard and I thought he played terrific.
"Even though we didn't win that game, I thought he had an outstanding game and I think that he is a good player and that's why we signed him and that's why we believe in him and are going to stay with him."
Greg Payne is a regular contributor to ESPNBoston.com.