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 it 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.”
Rotich has now been sent home from the Olympic Games in Rio.
“He is not going to be with the team anymore. He is someone who has messed up.
He has to carry his own sword,” Kip Keino, Chairman of the Kenyan Olympic Commitee, told BBC World Service.
Athletics Kenya vice president Fatma Awale said: “As a country and as a nation we are shocked and surprised with the new developments.
“We will wait for the investigations to take place so we can ascertain what is the real story to these allegations.”
Kenyan sports minister Hassan Wario added: “The timing is malicious. It’s aimed at demoralising our team.”
In the undercover operation, Mr Rotich was approached by a doping specialist hired to supply banned substances to a fictional British sports team, the Sunday Times reports.
In the film Mr Rotich appears to request a one-off payment to give the 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.