Originally Published: 27 JUN 22 07:42 ET

Updated: 27 JUN 22 12:18 ET

By Kylie Atwood and Kevin Liptak, CNN

(CNN) -- European and US officials do not expect that Turkey's concerns about Finland and Sweden joining NATO will be assuaged before the alliance's summit this week, US and European officials told CNN.

Yet some officials believe that Turkey may be eying the summit as a place to finally make agreements that could propel the process forward.

"My best projection based on what I've seen is that they will run this to the wire at Madrid. They also always prefer if they're going to make concessions to do it at the leader level, they believe that enhances that status," said one European official when discussing the matter. "It is Turkey's standard operating procedure not to give concessions till the last possible moment. And that last possible moment is usually defined as a bilateral with the US president, followed by a leaders meeting."

But Turkish officials have said that they do not see any "limited timetable" to the talks, and some US and European are less convinced that Turkey is ready to strike an agreement in Spain.

White House officials have been circumspect about whether US President Joe Biden and Turkish President Recep Tayyip Erdoğan will meet in Spain. But one person familiar with the matter said they expected the men to speak at some point about the accession process, though it may not be elevated into a formal bilateral meeting.

Speaking to reporters at the G7 summit in Germany, US national security adviser Jake Sullivan said the goal ahead of the Madrid summit was to "create as much positive momentum as we can behind the candidacies of Finland and Sweden," though he cautioned, "I am not sitting here today suggesting that all issues will be resolved by Madrid."

He said no formal bilateral meeting was scheduled between Biden and Erdoğan, but that they "may very well have the opportunity to see one another."

"Let's see how the next 24 hours unfold. There is a flurry of diplomatic activity occurring today," he said.

Biden, he said, was following the developments "very closely."

"His team is working it with the Finns, Swedes and Turks, and I'm on the phone daily with my counterparts," he said. "So, let's see how things go."

US officials have been wary about inserting Biden directly into the discussions, aware that having the US so closely involved could raise the stakes and escalate Erdoğan's demand -- including the likely extradition request for a US-based cleric Erdoğan accuses of orchestrating a 2016 coup attempt.

Still, US officials are still confident the applications from Finland and Sweden will eventually be successful.

Erdoğan has accused the two countries of harboring members of the separatist militant Kurdistan's Workers Party, also known as PKK, which Turkey views as a terrorist organization. Turkey also wants the countries to get rid of an embargo on arms sales to Turkey that was put into place after Turkey's military intervention in northern Syria in 2019.

As talks have lasted for over a month, US and European officials are growing quietly frustrated with how Turkey has drawn out what they initially hoped would be a quick entry to the defensive alliance for the two countries. Some officials are now concerned that Turkey may want more in terms of concessions than it is publicly stating.

"There is concern over the delay, and what else Turkey may begin to push for as they recognize the leverage that they have right now," said a second European official.

A lack of progress on the two countries joining late would put a damper on the high-profile gathering where leaders are looking for ways to bolster the defensive military alliance. In recent weeks, officials had stated a desire to have the challenge in the rear-view mirror by the time of the meeting in Spain.

At one point, officials privately said they hoped the Madrid summit would act as a welcoming party for the alliance's two newest members. It would have sent a clear message to Russia about NATO's growing capabilities.

"My intention is to have this in place before the NATO summit," NATO Secretary General Jens Stoltenberg said of the process to get Finland and Sweden to join NATO, as he stood next to Secretary of State Antony Blinken earlier this month. "At the same time, I know that to make progress we need 30 Allies to agree."

Last week Turkey met with officials from both countries and NATO, but there was no breakthrough after the meeting.

And meanwhile, with the ongoing war in Ukraine, Turkey has also been involved in some direct talks with Russia -- which ardently opposes NATO expansion -- about the need to get Ukrainian grain out of the country.