The bill is a key requirement for the east African nation, famed for its distance runners but tarnished by some 40 doping cases in recent years, to be declared compliant with the Wada code ahead of the Rio de Janeiro Olympics starting on August 5.
Kenya was given a deadline to enact the law or be declared non-compliant, which brings Wada sanctions, but the country's parliament goes into recess for 10 days on Thursday so the bill cannot become law before time runs out on April 5.
The sport's governing International Association of Athletics Federations (IAAF) said this month it was highly unlikely Kenya would be suspended from the Olympics but several sports leaders want president Uhuru Kenyatta to push the bill through.
