The tournament, which Zimbabwe has won for the last two years, is set to be staged from May 19 to June 1, 2019.
Sports Minister Kirsty Coventry said: “The deal was not good for Zimbabwe or for Zifa.
“We want to make sure that when we do host an event of this magnitude, that we are fully prepared, we have good timing. We just do not feel that that was really given to us this time around.
“Moving forward, we will continue to work closely with Zifa in terms of what the next steps are and what the future holds in terms of hosting the event.”
Zimbabwe won last year’s Cosafa Cup in South Africa, beating rivals Zambia in the final.
Zifa’s president Felton Kamambo echoed Coventry’s sentiments about their hopes of hosting future tournaments.
“As Zifa, our team will be participating in the Cosafa tournament, wherever it’s going to be held. We will try and bid for future hosting of Cosafa, that is maybe from 2021 going upwards, so that we have enough time, like the minister has said, to prepare to host this tournament,” said Kamambo.-Zimlive