The media watchdog is understood to be concerned that the colour of the runners' socks and the stripes on their shorts may cause viewers to compare the characters with Bedford, who has called for the ads to be taken off air.
Chris Moss, the chief executive of The Number, which runs the 118 118 service, confirmed there had been conversations with Ofcom.
Bedford, the former British 10,000 metres world record holder, who is now director of the Flora London Marathon, claims the 118 118 runners are based on his image which was used without his permission.
The Number insists the characters were inspired by the late US runner Steve Prefontaine. The Advertising Standards Auhority rejected a complaint from Bedford's lawyers last year.
Ofcom confirmed it was pursuing a complaint but declined to give details.
- Newsmaker, p12.