Griezmann joined Barca from Atletico Madrid in the summer of 2019, having established himself as one of the world's best forwards while winning the World Cup with France.
After firing at least 20 goals in each of the last six seasons, Griezmann scored just 15 times in 48 games in his first season for Barca, a disappointing haul given the €120m (£107m/$134m) fee required to bring him to the club.
The forward has yet to score in four appearances for Barca this season, all in La Liga, but Wenger says that he believes Griezmann still has his star quality.
However, having largely been played out of position since joining Barca, Griezmann is unable to shine, Wenger says, as he is forced to defer to Messi.
"Not playing at his position is complicated in the long term," Wenger told beIN SPORTS. "At the start, the guy accepts it but, if he does not meet his needs in the long term and he feels that the position does not allow him to express his qualities, he will become discouraged.
"Today, he is a player who must play in the centre because he has a great work rate, a precision in his passes. He can be dangerous with the last pass and by scoring goals, but there is congestion because he is in the range of play of Messi."
The Frenchman recently praised his national team boss, Didier Deschamps, for playing him in the right position during a hard-fought win over Croatia in a World Cup final rematch.
Griezmann remained on the bench in Tuesday's victory over Ferencvaros, with manager Ronald Koeman turning to Messi, Ansu Fati, Philippe Coutinho and Francisco Trincao in attack.
Sergio Busquets, Pedri, Ronald Araujo, Ousmane Dembele and Junior Firpo, meanwhile, were brought off the bench as Koeman used all five of his substitutes without turning to the former Atletico Madrid man.
After that match, Koeman stressed patience while adding that Griezmann could be involved Saturday when Barca take on rivals Real Madrid in El Clasico.