Wenger said: "Beckham will come in January to train with us. Occasionally, he will be with the first team and the reserves. He can give good advice while we will help him to be fit. It will be good.
"The youngsters look up to him. I admire how strong he has been mentally through his career. He has been through some tough times.
"But I respect the fact he loves football and he has always shown respect for his manager even when he was dropped.
"He did not come out in a silly or spoilt way. And he has delivered when it mattered. He showed toughness when he scored that free-kick against Greece right at the end.
"I had considered signing him in the past but he was at Manchester United for many years and it was always very difficult."