It is the second year running that a proposed friendly between the two clubs has not transpired, though on this occasion it is Liverpool who have pulled the plug.
The Merseyside club have decided against a trip to the southern hemisphere on the weekend of May 17-18 having expressed an interest in either Cape Town or the Indian Ocean island of Mauritius, but will now do neither.
According to supersport.com website, Ajax executive director Ari Efstathiou confirmed the news without giving reasons for the pull out.
It will be a great disappointment to the legions of local Liverpool fans, who would have no doubt traversed the country to see their side in action, especially as they come off a hugely successful English Premiership season in which they may yet be crowned champions for the first time in 24 years.
Liverpool had planned to play Ajax in Cape Town last May, but the PSL blocked the fixture as it fell within the domestic season. This time they have given the green light as the proposed date of May 18 is one day after the curtain comes down on the domestic campaign with the Nedbank Cup final, but the Reds have decided not to travel.