Kenya, a leading nation in long-distance running, missed a WADA deadline in February to implement new regulations in a country where about 40 athletes have been banned for doping in the last three years.
It needs to set up and fund a national anti-doping agency, among other things, which will be approved by WADA.
If Kenya is declared non-compliant its track and field athletes could miss out on the Rio de Janeiro Olympics starting in August.
Russian athletes have already been banned with the country struggling to become compliant in time for the Games.
"We understand funding is now available and they need to pass legislation, we know the type of legislation they are talking about which is acceptable," Reedie told reporters during an International Olympic Committee (IOC) meeting in Switzerland.
"They (Kenya) are very well aware of what they need to do. They need to reply to us by April 5.
"They simply need to do it. If they don't do it my compliance review committee will take the matter further and is likely to include, if nothing happens, a set period during which they must comply otherwise there will be a declaration of non-compliance."
Reedie said he was "hopeful" but added that it was up to the Kenyan government to deliver.
A top Kenyan athletics official said last month the world athletics federation IAAF, itself under pressure to get tougher on doping, was planning to ban Kenya from the Rio Games so "the world will understand how serious they are".
(Editing by Ed Osmond)
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