Editors at Britain's Daily Mirror newspaper allege the pair first met at Paris Fashion Week earlier this year (14) and have been dating for several months.
A source tells the newspaper, "They were introduced through mutual friends, and have the same social circle back in Los Angeles. They speak all the time and enjoy hanging out together, just doing what teenagers do. Both David and Victoria have given them their blessing."
The young couple were spotted skateboarding together in Los Angeles in June (14), but their romance is not thought to be serious as Beckham lives in London while Moretz, who at 17 is two years Beckham's senior, is based in the U.S.