Beckham's eldest kid, Brooklyn, is a fan of the Gunners even though everyone else in the family are Manchester United fans - and Brooklyn trains with London rivals Chelsea.
"I have two sons who support Manchester United and one of them is an Arsenal fan," Beckham told French sports daily L'Equipe.
"By the way, I do not know how I let this happen!"
The 37-year-old said however that all three of his sons are now supporters of Paris St -Germain and has spoken of his joy at being able to play in front of his children.
"They always become fans of the teams where I play, so now they are supporters of PSG," he said.
"To be honest, one of the greatest joys of my career has been being able to live this life as a professional player with my children over the past decade.
"Even before I met my wife, it was a dream that I had when I was young. I wanted to have children living my life as a footballer with me.
"I am very happy. My daughter is only two years old, she does not yet know what being a footballer means but will she will realise one day."
Beckham, who impressed during his full debut against Marseille this week, also said that he has not signed for Paris St-Germain just so the club can sell some jerseys.
"I am very proud people buy my shirt, but I can still play a bit of football, I can assure you of that," he told the paper.
Beckham also said that United manager Sir Alex Ferguson is one of the reasons why he is still playing at the top despite his advanced age.
"The majority of the Manchester United players who started in the mid 1990s - Ryan Giggs, Nicky Butt, Gary Neville, Phil Neville, Paul Scholes and I - are still playing.
"I think it is because Sir Alex Ferguson showed us the way when we were teenagers. He taught us to respect the game, to respect our body and to love what we do."
And despite playing with such consummate professionals, Beckham stated that his current team-mate Zlatan Ibrahimovic might just top them all in terms of desire and work rate.
"I have only been at the club three weeks, but I haven't met many players in my career who are as professional as Zlatan.
"Ibra is a great example for everyone. He thinks football, he lives football, but he continues to work hard and he wants to win all the time. When he loses a little game, his face drops - it's impressive."