Griezmann, 29, started Barca's first three league games this season on the right of a three-man attack but returned to a central role while on international duty with France.
After scoring in Wednesday's 2-1 win against Croatia, he said he felt good while representing his country because national team boss Didier Deschamps "plays me in my best position." The comments were reported in Catalonia as a criticism of Koeman.
Speaking at a news conference on Friday, Koeman said he has "no problem" with Griezmann but told him to focus on delivering on the pitch rather than worry about his position.
"I spoke with Antoine [on Thursday] and I told him I'm looking out for the best for the team and I think he's best on the right for us," Koeman said.
"He can play in three positions. He could also play as a No. 10 or a No. 9. In fact, when I was the Dutch coach, in a game against France, he played on the right.
"I have no problem with Antoine. I can only play one No. 9, one No. 10, one No. 7 etc. I don't play players out of position. Griezmann can play wide coming inside on his left foot. If he has another position that he likes more, that's how it is, but we can't have 10 players in the No. 10 role.
"I decide based on what's best for the team. The coach is in charge and the players must be at their best when they play."
Griezmann is yet to score for Barca this season and was singled out by Koeman for missing two chances in the draw against Sevilla before the international break.
He will have another chance to get off the mark when Barca travel to Getafe in La Liga on Saturday.
"It has been good for his adaption to have Dest here for these last two weeks and not with the national team," Koeman added. "We had time to talk about the system but that system is not different to what he played at Ajax.
"It's a possibility he will start [against Getafe]. It's good to have him because he is one of the players who will be the future of this club."
As well as Alba, Barcelona are also without injured goalkeeper Marc-Andre ter Stegen against Getafe. Koeman said it is unlikely the Ter Stegen will be ready for the Clasico against Real Madrid next week.
"Messi could play the next four games," Koeman said when asked if he may need resting. "He is one of those players that gets more tired when they don't play."