Ads for foods considered unhealthy are already banned on children's television, but not online.
The Committee of Advertising Practice (CAP), which sets the rules for advertisers in the UK, will soon launch a public consultation on the issue.
A ban could affect content on services such as YouTube and ITV Hub.
In 2007, the broadcasting regulator Ofcom introduced strict rules banning the advertising of food high in fat, sugar and salt (HFSS) during television programmes likely to appeal to under-16s.