Turkey is using the possibility of a contract for a new missile defense system worth billions to rebuild its relationship with Russia, a move experts say could signal that Turkey is no longer interested in being a NATO member.

In 2013, Turkey selected a Chinese company to build its first long-range air and missile defense system, rejecting bids from U.S., European and Russian companies. After facing pressure from NATO over concerns about connecting to the alliance using Chinese infrastructure, however, it rescinded the contract, saying that it would instead use Turkish companies to develop and build the defense system.

But this week, Turkish President Recep Tayyip Erdogan reportedly invited Russia to resubmit its proposal, which was deemed too expensive just three years ago. Michael Rubin, a scholar at the American Enterprise Institute, said he expects the American and European countries to resubmit their bids as well, meaning the U.S. team of Raytheon and Lockheed Martin as well as Eurosam will also be part of the process.

In the first go-around for the $4 billion tender, Turkey selected a bid from the China Precision Machinery Export-Import Corporation. The Italo-French Eurosam offered its Aster 30 missile, Raytheon and Lockheed bid the Patriot Advanced Capability-3 system, and Russia offered the S-400 via its state-run Rosoboronexport.

Michael O'Hanlon, an analyst at the Brookings Institution, said he had "absolutely no doubt" that the move is driven by politics, not technical issues.

Turkey's relationship with Russia has been shaky since last year, when the Turkish Air Force shot down a Russian fighter jet along the border with Syria in November 2015.

Tom Karako, a senior fellow with the Center for Strategy and International Studies, said the move to rebid the contract is driven by a desire to "kiss and make up" with Russia, but added that a contract with the Russians would likely be worse received than the 2013 award to China.

"Here we are having Russia poking the eye of various European neighbors and other NATO allies. If Turkey decides in the midst of all that to get in bed with Russia on missile and air defense, it would make the next NATO summit sort of like an awkward Thanksgiving dinner," Karako said.

"If they want to get in bed with Russia, that's a signal they're really not that interested in being part of Europe or being part of NATO," he continued.

In addition to improving its relationship with Russia, Turkey is also likely looking to "play hardball" to get things it wants that are totally unrelated to the contract, like the extradition of Fethullah Gulen, who Turks suspect is behind the attempted coup, from the U.S., Rubin said. He said Turkey will not select the U.S. bid if America can not deliver on this demand, as well as ending support to the Syrian Kurds, who Turks view as a terrorist group.

"It may not be written directly into the contract, but it's sort of a quid pro quo," Rubin said. "What Erdogan doesn't understand is there's rule of law in the U.S. and [President] Obama or [Defense Secretary Ash] Carter can't simply say we're going to extradite Gulen. Erdogan has no idea how it works."

Karako said an effort to blackmail the U.S. into doing what it wants with the bidding process is "a very bad miscalculation."

Rubin also said that a closer relationship between Russia and Turkey, who is a partner in the development of Lockheed Martin's F-35, could put newly developed American technology at risk if the Turks share with the Russians "out of spite."

The best possible outcome, Rubin said, is a repeated bid and rebid processes that will go on until Erdogan is out of office or "comes to his senses."