France star Griezmann, a €120million signing from Atletico Madrid last year, has struggled to impress on a regular basis alongside Lionel Messi at Camp Nou.
The forward, who missed a penalty against Real Betis last week before scoring in Barca's 5-2 victory, has just two goals, one assist and four chances created to his name in seven LaLiga appearances this season.
Koeman thinks the 29-year-old is bound to hit top gear, though, as long as he maintains his strong work ethic.
"He needs a bit more confidence and scoring goals always gives you that confidence," Koeman told Mundo Deportivo.
"You can't say he doesn't work, he works a lot, but maybe he feels a little more free when he's with the national team, having been with them a long time and always playing in the same position.
"There's are many more things besides, but a player who is working and trying so much to change things, I think in the end he'll get to where he wants to be.
"His best position is maybe more central, as a number nine, a number 10 behind a nine, with a lot of freedom on the right wing cutting in, with [Ousmane] Dembele playing more outside.
"They're positions in which he can give a lot to this team."
With Griezmann out of sorts and Ansu Fati sidelined for four months after meniscus surgery, Barca have been tipped to make a new move for Lyon forward Depay.
The Catalan club agreed terms with Depay during the previous transfer window but a deal could not be struck between the clubs, and the Ligue 1 side's president Jean-Michel Aulas insists they will not sell the player in January even though his contract expires at the end of the season.
However, Koeman will not discount the prospect of signing the Netherlands international, with whom he worked while in charge of the national side and who has been directly involved in eight goals in Ligue 1 this season, a tally bettered only by Kylian Mbappe.
"Now is not the moment to talk about players who aren't here. For me, it's not good," he said.
"It's true his name has come out and he's played every game with our national team as a number nine.
"Everyone can have their opinion, but not here, and we'll see what happens in the future."
Koeman also suggested a deal could yet be struck to sign Eric Garcia from Manchester City, adding: "Well, I don't know. It depends on Manchester City."
Speaking to Sport, Koeman admitted captain Lionel Messi had been "unhappy" when he first arrived at the club, the forward having tried unsuccessfully to leave in the wake of the 8-2 Champions League destruction by Bayern Munich, a club-record defeat in the competition.
Messi's form has been questioned in 2020-21, the Argentina star having failed to score from open play or register an assist in his first six LaLiga matches.
He produced a star turn off the bench against Real Betis, however, scoring twice, assisting another and playing a key role in Griezmann's goal as Barca claimed a 5-2 victory.
"I spoke to him on the first day, totally frankly, and I've never doubted him," Koeman said of the six-time Ballon d'Or winner.
"I see him training every day and enjoying playing. I said on the first day that he's the best player in the world and of course I prefer to have the best in the world in my team.
"As I said after the game against Betis, if he's well, he'll always start."