MEPs meeting in Strasbourg will vote on Thursday on a resolution calling for a temporary suspension of talks.
This follows what many say is the deteriorating state of Turkish democracy and human rights following the attempted coup of 15 July.
In the resolution, MEPs condemn the coup attempt but also express concerns at the "ongoing oppression" of Turkey's Kurdish population, which has seen lawmakers and others, including journalists, forcibly removed from office and in some cases detained.
Earlier this week, the Socialist group called for talks to be frozen temporarily while, last week, the EPP group went further, demanding a complete suspension of negotiations.
Ahead of Thursday's vote, Greens/EFA group MEP Ernest Maragall, a member of the European Parliament's Turkey delegation, told this website, "We are gravely concerned by the deteriorating situation in Turkey in respect of human rights and the rule of law.
"We have condemned the attempted coup of 15 July and support Turkey's right to bring those responsible to justice. But what we are now seeing is the regime using this as cover to arrest, detain and harass a vast number of its opponents whether or not they had anything to do with the coup."
He added, "Regrettably we now find it necessary to send a strong signal to the Turkish government by temporarily freezing EU accession talks."
The GUE/NGL group, meanwhile, says that democracy and the human rights are "in freefall" in Turkey, with its members urging EU leaders to "immediately halt the controversial migrants deal and to re-examine all ties with the Erdoğan regime."
Under the EU/Turkey deal, Ankara will receive financial aid from the EU in return for Turkey's efforts in tackling the migration crisis. The EU has also promised to liberalise visa arrangements for certain groups with Turkey.
But Takis Hadjigeorgiou, a Vice-Chair of Parliament's delegation to Turkey, said the EU's relations with Turkey has reached a critical juncture, adding, "The European Parliament would have risked losing its last shred of dignity had it not proceeded to having this debate on Turkey and a vote on the resolution this Thursday.
"Meanwhile, we must also underscore the arrest of the HDP's Selahattin Demirtaş - the co-leader of the third biggest party in the country which represents at least six million voters."
Swedish MEP Malin Björk agreed, saying, "political will is badly needed if the EU is to face up to the situation in Turkey. First of all, we call for an immediate stop to the shameful refugee deal with Turkey."
More comment came from UK MEP Syed Kamall who, speaking in Parliament on Tuesday, called for the EU to have a "new and more honest relationship with Turkey."
Kamall, leader of ECR group, said that the Turkish governing AK Party "still contains many elements that are seeking to marry together Islam, democracy and economic liberalisation, but that Erdoğan's actions have raised sufficient concerns for most MEPs to unite in saying, 'enough is enough'.
"ECR has members that are for, against, and agnostic on the issue of Turkish membership. But we can all see that the current relationship is not working.
"So instead of business as usual, let us build a new relationship based not on false promises, but on honesty."