Beckham is currently without a club after leaving Los Angeles Galaxy at the end of the Major League Soccer season and has told Wenger he has not trained since. The Frenchman is unsure of Beckham's fitness, but believes the 37-year-old would not have taken an extended break if he wanted to win a contract with the Gunners or any Premier League side.
"He told me that he doesn't look at all to be in shape," Wenger said. "Beckham is super-ambitious. If, in his mind, he wanted to play in the Premier League he would not have gone on holiday. He would have prepared and come in and tried to impress me. He told me he has done nothing at all."
It is still to be determined whether, and where, Beckham will continue his career.
Wenger declined to speculate on whether Beckham could still perform in England's top flight and insisted a permanent deal for the former Manchester United, Real Madrid, LA Galaxy and AC Milan midfielder is not under consideration.
"That is not on the agenda," Wenger said. "He asked to come here to get fit. (It's) purely for fitness. There's no speculation about signing or anything. Maybe in June he has plans to play somewhere."
Beckham called Wenger to request a third spell training at London Colney after previous stints in January 2008 and December 2010, which came before a lengthier spell with Tottenham in January 2011.
Former Gunners Thierry Henry and Sol Campbell have also returned to the club for training periods and Wenger believes Beckham sets a good example to his young squad.
"He's fantastic," Wenger added. "The young English players look at him and take his advice on board. His positive advice. This guy has a fantastic quality, has done the maximum of his career that you can do. Why? Because he loves football. After training he stays and plays."
Beckham's arrival had an immediate impact, with photographers waiting outside the training ground for his arrival. Wenger joked: "I thought 'What's happening today?' Oh yes, Beckham is here."