The Asian Football Confederation (AFC) told member federations and potential bidders, including Australia, on Thursday that it had been asked by the global governing body FIFA to move the tournaments to even-numbered years.
The news came after the AFC had in February announced a list of interested candidates, including Australia, Kuwait and South Korea, who were keen to host either edition of the tournament.
India and Indonesia also wanted to stage the 2031 event, while a joint-central Asian bid was also being put together by Kyrgyzstan, Uzbekistan and Tajikistan.
Japan had also announced it wanted to host the 2035 event.
In a letter to its members, Asian soccer bosses reported that FIFA had told the AFC of "anticipated" changes to the international match calendar, and how it wanted the men's Asian Cup to now be staged in even-numbered years.
The AFC said "following careful consideration" it had agreed to FIFA's request and bidding for both the 2031 and 2035 competitions would "be abandoned in its entirety."
It seems likely the Asian Cup would be pushed back a year to 2032 and 2036 to align with when the other major continental showpieces, the European Championship and South America's Copa America, are played -- but nothing has been confirmed.
"As the AFC works through the implications of this adjustment and considers the necessary revisions to its competition calendar, we believe it is considered appropriate and necessary to discontinue the current bidding process in order to avoid uncertainty in the hosting arrangements," the letter said.
"Once these considerations have been finalised and a new bidding process is launched, we trust that we may continue to count on your full support and participation."
Australia is currently staging the women's Asian Cup, with the hosts having reached the final this weekend.
The next men's Asian Cup will be staged in January 2027 in Saudi Arabia.
The last time Australia hosted the men's Asian Cup ended with Ange Postecoglou's side lifting the trophy back in 2015.
With agencies