NYCFC sporting director Claudio Reyna said finding a suitable stadium solution for the club remains a "top priority" but wouldn't say if a permanent plan is imminent.
The club has shared Yankee Stadium since beginning play in MLS in 2015, and has repeatedly stated it prefers a different site in New York City proper.
"We continue to explore a few options ... It's absolutely a top priority for the club and we know it's an important decision," Reyna told ESPN FC's Herculez Gomez.
Since it entered the league, the club has attempted to secure a site for a soccer-specific stadium. Various sites in Queens and The Bronx have been reportedly considered, as well as Belmont Park in nearby Elmont.
"We have to get it right, it's a decision for the next 50 years for this club," the former U.S. men's national team captain said. "Theres a lot of work going into it, it's extremely important."
The atmosphere at NYCFC's home games at a baseball stadium has been criticized for the sightlines and the layout of the pitch.
"We love the support we are getting when we play at Yankee Stadium, but look forward to having a stadium for sure," Reyna said.
NYCFC visits the LA Galaxy (Saturday, 4 p.m. ET on ESPN) and currently sits in sixth place in the Eastern Conference standings.
"It was difficult throughout the year, as conversations were going on whether he was going to retire or not," Reyna said. "We had to be mindful of the next steps when you build a team."
Villa, who now plays at Japanese side Vissel Kobe, scored 80 goals in 124 MLS appearances for NYCFC.