Messi picked up a groin problem while on international duty earlier this month, but did not miss any club football and aggravated the injury in Barcelona's 1-1 draw with Atletico Madrid on Wednesday night, which has left him facing three weeks on the sidelines.
Bauza has claimed that the Catalan giants "are not taking proper care" of Messi, but Enrique says that he would "rather not get involved in the merry-go-round of rumours" after being asked about Bauza's comments.
"The only truth in this story, because there are a lot of different opinions floating around, is we all seek the best for Messi and all the other players in the club," Enrique told reporters.
"That's the objective we are all looking for. It's always bad news when a player gets injured, dreadful news. The best player in the world getting injured is bad news for us and anyone who enjoys watching good football. But I would rather not get involved in the merry-go-round of rumours that would only aggravate the situation further."
Barcelona currently sit third in La Liga ahead of Saturday's trip to Sporting Gijon.