The Costa Rica international has been on loan in four straight seasons since joining Arsenal from Deportivo Saprissa in 2011.
With injuries hitting Wenger's squad, Campbell has been given his chances, making three Premier League appearances and four in Europe.
Wenger said he was impressed by the 23-year-old's qualities and feels Campbell is ready to be a regular, even when the likes of Aaron Ramsey and Alex Oxlade-Chamberlain return.
"This season I didn't want to give him out because he has a genuine team attitude and he's a fighter," the Frenchman said.
"What you want from him is to bring more offensively when he played and recently he has shown when he is confident he can produce the offensive quality as well being reliable on the team attitude.
"He's a fighter so that's great for us. I smelt something with him that is very interesting.
"The other night he has a positive attitude, he was not only playing safe."
Wenger ruled out sending Campbell away from the club again, insisting the 55-time international was now ready for the competition.
"I'm very keen to keep him here. A guy who comes here very young from Costa Rica, he has a learning process to the competition. Week in, week out to fight every week," he said.
"At the end of the day, you decide what's best for the team.
"Ramsey is coming back, of course, Alexis Sanchez being there, but it's good to move Ramsey inside during a game and give Campbell the opportunity as well."
