Long Bridge Park, along the Crystal City neighborhood in Arlington. (Evy Mages/For The Washington Post)

Arlington County and the city of Alexandria are considering jointly building a long-delayed aquatics and fitness center at Arlington’s Long Bridge Park and will ask residents in coming months whether they would support it.

If Alexandria goes along with the idea, its $20 million plan to expand the Chinquapin Park pool, next to T.C. Williams High School, would be set aside. It has not been determined whether or how the two neighboring communities would split the cost of construction and operation of the Long Bridge pool.

“We’re dipping our toe in the waters about a partnership,” said Mark Schwartz, Arlington’s acting county manager. “The surveys will let us know what the public thinks . . . and the contours of the partnership would have to be worked out.”

As part of a regularly scheduled survey about civic issues in Alexandria, a random sampling of residents will be asked this week whether they are interested in the idea, said James Spengler, Alexandria’s director of parks and recreation.

Arlington residents will be asked a similar question this fall as part of what Schwartz said will be a statistically valid sample poll as part of the update to the county’s public-spaces master plan. If there’s enough interest, both governments will negotiate how such a partnership could work. Schwartz said there’s no timeline for when negotiations would be completed.

Alexandria and Arlington cooperate on several projects, including the development of the Four Mile Run greenway and the connections between Alexandria’s bus rapid transitway in the Potomac Yard area and a similar transit project through Arlington’s Crystal City.

The Long Bridge pool complex was put on hold in late 2013 after construction bids came in $3 million above the $79.5 million that Arlington budgeted. The county then pinned its hopes on the Washington area winning the competition to host the Olympics, expecting that a private party would help finance the construction. That didn’t work out, either.

The pool complex became an issue in the 2014 County Board elections, when then-candidate John Vihstadt (I) used it as an example of overspending on capital projects.

Three-year-old Long Bridge Park is built on reclaimed industrial land in Crystal City, between Interstate 395 and railroad tracks. The park’s expansion was supposed to be financed by the proceeds of two voter-approved bond sales and $15 million from the real estate company Vornado Realty Trust, the county’s biggest taxpayer.

It is now the site of the county’s Fourth of July celebration, and its athletic fields are in constant use, including by Marymount University’s soccer and lacrosse teams. In June, the County Board voted to build a $1 million playground, which has been designed by local children, at the south end of the park.

If the aquatics and fitness center is built, its plans call for the Olympic-size competition pool, a teaching pool, a family leisure pool with slides and a “lazy river,” an indoor fitness area and eight acres of outdoor space. A popular esplanade that is in use would be expanded, and eight acres of new parkland would be designed as spaces for festivals and large gatherings.