The Sunday Times and German broadcaster ARD secretly filmed Major Michael Rotich apparently making the offer.
But he told the newspaper he was only going along with the sting because he wanted to find out who the undercover reporters were and "protect" athletes.
The Anti-Doping Agency of Kenya confirmed it will look into the report.
Chief executive Japhter Rugut said: "ADAK will investigate, verify and authenticate this new allegation."
BBC Sport has contacted Athletics Kenya but is awaiting a response.
In the film Rotich appears to request a one-off payment to give athletes 12 hours' advanced notice of a pending drugs test because he knew the official anti-doping testers.
Kenya was only removed from the World Anti-Doping Agency's list of "non-compliant" countries on Friday.
The country twice failed to meet Wada's requests for anti-doping mechanisms to be put in place, with athletes facing special testing before the Rio Games, which opened on Friday.
More than 40 of its track and field athletes have failed doping tests and been banned since 2011.