The former Manchester United man said it was the Arsenal boss who influenced his son.
"I tried to get Man United shirts on them early," Beckham said.
He added: "Actually, I do know how it happened. I took him to an Arsenal game and Arsene Wenger treated him so well, gave him a shirt with his name on the back
and his favourite number.
"I had that when I was a kid with Man United. I let them support whoever they want. They don't have to support the teams I played for."
Beckham maintained his fitness by training with Arsenal in 2008. Last year, Beckham's former club AC Milan beat Arsenal 4-3 on aggregate in the Champions League last 16.
"When I found out that my son, Romeo, supports Arsenal, I became disappointed," the midfielder said before the tie.
"I can't bring myself to support Arsenal, although I do respect the club. I am convinced that Milan will go through."