The couple are parents to Brooklyn, 12, Romeo, nine, Cruz, six, and baby Harper. But it seems that they would like their own five-a-side - or more - team.
In an interview for Jonathan Ross's ITV1 chat show tonight, Beckham said: "Harper is seven months now. I can't even look at her without welling up.
"After having three boys, you just assume that you're going to have another boy, but when we got told she was a little girl, it was amazing.
"We might have one more or two more, you never know. We're not thinking about it yet, but if it happens, great. We're enjoying the kids as it is. It's always a thought.
"I mean, we're busy people and we're enjoying the four kids that we've got already and we're lucky, we're lucky to have four healthy children."
Beckham said that despite their hectic lifestyles at home in Los Angeles and travelling the globe - he's in London for the launch of his H & M underwear range and fashion designer Victoria has been modelling - both he and Victoria try to do 'normal things' with the children.
He said: "You know, we take them to school, we pick them up. We take them to taekwondo or wherever they go, so we always do the activities with them."
Although the sportsman has another agenda when it comes to teaching his sons martial arts - protecting their little sister.
"I just want them to protect her when she's at that age. At that age when she needs protecting. Cruz does taekwondo, Brooklyn does boxing and Romeo does karate, so they'll all be ready.
"But Cruz is the one who's going to really look after Harper, he's the tough one."
As well as marital arts, the boys are understandably keen on football, the game which made their father famous. Although David admits he gets a bit too involved from the sidelines.
He said: "I was watching the kids play the other day, it was the game just before they were playing. It was the younger kids of Romeo's club, and they're playing in the game and there was a penalty given. And the kids are seven years old and he sent the kid off.
"And I was like, 'Come on, he's seven years old, referee, you can't send him off.' And he looked at me and was like, 'Yes, I can.' And I was like, 'OK, well, you can't, he's seven years old.'
"And he came over and gave me a red card. He told me to get out of the park. For real. The gate was only 20 yards away and I waited and went back in when my son's game was on."
David, who appeared on the chat show with singer Jessie J and comedian Kevin Bridges, also spoke about the fact that despite being happy in Los Angeles, the family will always be proud of their British - and particularly his East End - roots.
He said: "My children have been happy for five years there, they're stable there. They're loving life there. My eldest is 12 years old now, he needs stability, so we did it for that, but we also love living there.
"But my boys, they love coming back to London, they love pie and mash. They did turn their nose up at liquor it's not the most attractive gravy. But it's amazing. All the boys, apart from Cruz, have the liquor. None of them have touched the jellied eels yet!"
The Jonathan Ross Show will be shown tonight on ITV1 at 9pm.
If you could afford to, would you want - or have wanted - more children?
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