WADA said last week Jamaican prime minister Portia Simpson-Miller had invited a special team to inspect the country's anti-doping authority but the global body was "unhappy" the visit could not be arranged this year in the wake of a string of drugs offences involving local athletes.
"The current position is unacceptable to WADA and we're not going to take it lying down, their suggestion that they'll talk to us next year," Fahey told the Daily Telegraph.
"To suggest to WADA they're not ready to meet with us to talk about their problem until some time next year is unsatisfactory, it's totally unacceptable to me and we shall act appropriately within an appropriate time frame."
Former world 100 metres record holder Asafa Powell, twice 200 metres Olympic champion Veronica Campbell-Brown and London Games 4x100 relay silver medallist Sherone Simpson all failed drug tests and were left out of Jamaica's athletics team for the world championships in August.
The credibility of Jamaica's anti-doping work has been further called into question by Renee Anne Shirley, a former senior official with the country's anti-doping agency, who told Sports Illustrated in August the authority had carried out just one out-of-competition test from February 2012 to the start of the London Olympics in July.
The Jamaica Anti-Doping Commission has denied any problem and questioned Shirley's character.
Fahey stopped short of threatening sanctions but said there were "a number of options" open to WADA.
The most severe would be to declare Jamaica "non-compliant" with the WADA code, which would pave the way for global sports bodies like the International Olympic Committee or international federations to impose punitive measures.
Only WADA code-compliant sports can participate in the Olympic Games.
JADCO were not immediately available for comment.
- Sports & Recreation