Oxlade-Chamberlain has finally made his playing comeback from the knee injury that kept him out of Euro 2016, with Gunners boss Wenger optimistic on the 22-year-old's full recovery.
The England forward hit the net as Arsenal saw off Chivas de Guadalajara 3-1 on their USA pre-season tour, with Wenger then challenging his player to realise his rich promise in the coming campaign.
"This is a very important season for Alex," Wenger told Arsenal's official club website.
"He was out for a very long time, I'm cautious with him at the moment but he's getting better in every game and that's good to see."
Oxlade-Chamberlain suffered a knee injury in Arsenal's 2-0 home Champions League loss to Barcelona on February 23
The 24-cap England man has been accelerating his recovery across Arsenal's pre-season however, with Wenger now expecting a fruitful term ahead.
"Power and penetration - he has it all," said Wenger.
"That's why I would like him to get to the level he can go to.
"Maybe he doesn't completely believe himself how good he can be and that's the final step for him."
Arsenal will conclude their pre-season schedule by facing Manchester City in Gothenburg on Sunday, before opening their Premier League campaign against Liverpool at the Emirates Stadium on August 14.
Wales star Aaron Ramsey and Chile's Alexis Sanchez are expected to feature against Pep Guardiola's side in Sweden, with both then in contention for the league opener.
Source : PA