Martinelli burst onto the scene after arriving from Brazilian fourth-tier side Ituano for £6 million in 2019.
His debut season ended with 10 goals in 26 appearances as optimism grew over his future at the Emirates.
But after signing a contract extension in July 2020, a serious knee injury kept the Brazilian sidelined until the end of the year.
Martinelli scoring against Crystal Palace last season
Manager Mikel Arteta was forced to defend his usage of Martinelli towards the end of last season, stating: "If there are any doubts, I love Gabi so much. More than all of you together!"
Martinelli will miss a significant portion of Arsenal's preseason as he competes for Brazil at the Olympics, but Winterburn doesn't believe that will impact his season.
Speaking to TribalFootball.com, on behalf of NetBet, the Gunners great said: "There's huge potential there which has been disrupted by injuries and I think next season he will get a lot more game time.
"He'll get a good pre-season under his belt, I'm not aware of any issues he has at the club which would obviously change things if he was pushing for a move away.
"I don't see why he wouldn't be at Arsenal next season and get more game time provided he stays fit."
Winterburn added on Martinelli's best position: "Most of the time he's played in a wide area and on occasions we've seen he can play through the middle, but I don't know which one he suits more as of yet."