Journalists gathered at El Prat airport in the Catalan city this week to ask Messi about comments made by Griezmann's former agent Eric Olhats, who accused him of running a "regime of terror" at the club.
Messi, who had just landed back in Spain from international duty in South America, snapped back that he was "fed up of always being the problem [at Barca]."
"I can understand why Leo would be angry," Koeman said in a news conference on Friday ahead of the weekend's game against Atletico Madrid.
"I think we have to respect people like Leo Messi much more. After such a long flight, to ask him things about Antoine when he lands shows a lack of respect.
"So, I have to defend Leo. If that happened to me after a 15-hour journey and a one-hour wait at the airport, then you go outside and there are press asking those questions, I would be dangerous and hating them as well.
"It's an attempt from [the media] to create controversy where there is none. I have not seen any problems between Leo and Antoine. In addition, the comments are from someone who's not been [Griezmann's agent] for years. It is complete nonsense."
Griezmann has always maintained that his relationship with Messi is good and sources close to the France international have told ESPN it has been years since he spoke with Olhats.
However, Messi's comments during the week have re-opened the debate about his future at Camp Nou after he unsuccessfully tried to leave the club following the 8-2 Champions League defeat to Bayern Munich in August.
Koeman initially said "no" when asked if he could see Messi -- who can walk away free when his contract expires next June -- leaving, but later conceded the final decision lies with the forward.
"Leo has this season left on his contract," he added. "I hope his future [beyond that] is here, but it is not me who has to convince him to stay.
"It is unbelievable what he's done for this club. But he's the main person to make decisions about his future. No one else can say what will happen in the future."
Messi returned to training on Friday as Barca prepared for Saturday's game against unbeaten Atletico Madrid in La Liga at the Wanda Metropolitano.
Atletico will be without former Barca striker Luis Suarez, who tested positive for coronavirus this week, but Koeman is also missing several players.
Sergio Busquets, Ansu Fati, Ronald Araujo and Samuel Umtiti are all sidelined with injuries, although Philippe Coutinho is available for selection again following three weeks out with a hamstring problem.