EVERETT — Members of the Boeing Co.’s Machinists union could have a say in where the company locates its second 787 assembly line.

Local Machinist president Tom Wroblewski reacted Thursday to speculation that talks with Boeing include implementing a “no-strike” policy in the Puget Sound region in exchange for the second line or for production of future Boeing planes.

“If these ongoing discussions produce anything outside of the current contract language, it will be brought to the membership and voted on,” Wroblewski said, in a statement. “Our members have the final say.”

After a 57-day strike last fall, Boeing and the Machinists agreed to a four-year contract. Since then, Boeing bought out its 787 supplier in Charleston, S.C. Boeing chief executive Jim McNerney confirmed Wednesday that the company has narrowed its second 787 line site list to Charleston, where workers recently decertified their union, and Everett, the location of Boeing’s original 787 line.

With a Boeing board meeting set for next week, and permits for a potential Charleston factory expansion set to start Nov. 2, time is running short for Boeing and its Machinists union to reach a compromise, local leaders say.

“It is critically important that the Boeing Co. and union continue their discussions as it relates to improving their relationship and keeping the 787 line in Everett,” said Ray Stephanson, mayor of Everett.

Stephanson sees plenty of reason for putting the second assembly line at Boeing’s existing factory in Everett. The state already has made its pitch for the second line. Washington lawmakers offered more than $3 billion in tax incentives to land the original 787 line in 2003.

“Clearly Everett has made its case from a business perspective,” Stephanson said. “Everything is ready here.”

Snohomish County Executive Aaron Reardon believes there’s more significance for the region than just the second 787 line. If Boeing and the Machinists can’t repair their relationship in time to keep the second line here in Everett, then Reardon sees the state’s aerospace industry declining and Washington losing out on Boeing’s replacement programs for the 737 and 777.

“It is critical that we do not let the second 787 line go to South Carolina,” Reardon said.

Boeing has relied on its members in Everett to fix problems created by its far-reaching 787 supply chain — a supply chain that has been blamed for its role in more than two years of delays to the lightweight, fuel-efficient jet.

On Wednesday, McNerney noted one of the company’s gripes with Everett: labor strikes. Work stoppages financially hurt Boeing and damaged its reputation with its customers, McNerney said. Workers in Charleston voted to decertify the union there in September.

“Some of the modest inefficiencies … associated with a move to Charleston are certainly more than overcome by strikes happening every three or four years in the Puget Sound” area, he said.

Boeing may face more opposition to South Carolina than just from its Machinists union. The company’s engineers union said Thursday that it would work to unionize the Charleston engineers should Boeing locate the second 787 line there.

“Certainly, we would mobilize if Boeing picks South Carolina,” said Bill Dugovich, spokesman for the Society of Professional Engineering Employees in Aerospace.