Getafe president Angel Torres revealed his side's interest in the Japan international this week and reports from Spain suggest the Madrid-based club are close to striking a deal.
Speaking after his side's victory against Levante, which moved Villarreal up to fourth, Emery admitted it is likely the winger will move on.
"I asked Kubo if he wanted to stay or leave [Villarreal] and he told me that he is looking for a way out," he said at his post-match news conference.
"Take's behavior is good, he has helped us and he must continue to grow as a player.
"However, he told me he wants to leave in order to find more minutes elsewhere and that's why he wasn't in the matchday squad today."
Kubo was snapped up by Madrid from FC Tokyo in 2019 and spent last season on loan with Real Mallorca, where he enjoyed more success than his current spell with Villarreal.
He scored four and assisted four more in 35 appearances but was unable to save Mallorca from relegation in their first season back in the top tier.
The 19-year-old has been used 19 times in total by Villarreal this season, 13 of those appearances coming in LaLiga.
However, Kubo has failed score from his eight shots, five of which were on target, and has yet to assist a team-mate or so much as play a successful cross from open play.