The EU warned membership candidate Turkey on Monday of a review and possible "redefinition" of ties after a referendum granted President Recep Tayyip Erdogan extra powers.
The warning from Enlargement Commissioner Johannes Hahn came days before ministers from the 28 European Union countries are due to discuss the bloc's troubled relationship with Ankara.
"The time has come for a thorough assessment of EU-Turkey relations and perhaps redefinition," Hahn said.
The "current situation is not sustainable, neither for Turkey nor for us," he said.
"All options are open, including continuation of accession talks, of course. But for the latter, Turkey has to fulfil the criteria."
Hahn, an Austrian, added that this could included a "a new format of cooperation", for example an upgrading of the customs union between the EU and Turkey.
He said he would personally prefer to keep the door open for Turkey, which applied to join the bloc in 1987 but has seen its membership bid stall over issues of democracy and human rights.
The EU has criticised Erdogan's referendum earlier this month which approved sweeping constitutional changes boosting Erdogan's powers.
Erdogan's suggestions that he could hold a new vote on reviving the death penalty would be the final blow to any chance that the EU could still let Turkey join.
The EU effectively suspended Turkey's membership process at the end of last year, saying it would open no new "chapters" -- issues for negotiation -- in its accession bid for the foreseeable future.
Turkey has meanwhile threatened to tear up a deal aimed at keeping migrants away from European shores.