According to Radio New Zealand, Key made the remark to students in the city of Dunedin.
Kay's son met the 37-year-old former England captain when the Los Angeles Galaxy team played an exhibition match in Auckland and was less than impressed with his intelligence.
Beckham travelled to New Zealand for the game against an Oceania All Stars Team.
The prime minister's office has refused to comment further on Mr Key's comments.
A selection of quotes that have been attributed to Beckham in the past, include:
"My parents have been there for me, ever since I was about seven."
"Well, I can play in the centre, on the right and occasionally on the left side"
"I remember so clearly us going into hospital so Victoria could have Brooklyn. I was eating a Lion bar at the time."
"Maths is totally done differently to what I was teached when I was at school."
"I'd like to have Brooklyn christened, but I don't know into what religion yet".