The 19-year-old was a regular for the Yellow Submarine during the 2021-22 campaign, making 40 appearances in all competitions, contributing seven goals and four assists in the process.
Pino only signed a new deal with Villarreal last November, which is set to run until June 2027, with the current agreement including a release clause of €80m (£66.6m).
However, there has been a host of speculation surrounding the Spaniard's future this summer, with a number of English clubs believed to be interested in his signature.
Arsenal are thought to be at the head of the queue, but Liverpool, Manchester City and Manchester United have also been linked with his services.
Emery has admitted that Villarreal would be forced to sell Pino during this summer's transfer window if they received a suitable offer.
"If an offer arrives for players like Yeremi Pino, then he will have to leave. We have a responsibility with the club. It is what it is," Emery told reporters ahead of the new La Liga campaign.
A recent report claimed that Villarreal would consider offers between €40m (£33.9m) and €50m (£42.3m) for the four-time Spain international in the current market.
Real Madrid are also believed to be long-term admirers of the attacker, who has scored 14 goals and registered five assists in 77 appearances for Villarreal since making the breakthrough into the first team.
Pino largely operates as a right-sided forward, but he is also capable of playing through the middle and off the left, featuring in a number of positions last term.
Arsenal are believed to be determined to add another attacker to their squad before the end of the transfer window, with the Gunners looking to challenge for a return to the top four this season.
Man United are also in the market for a forward, with new head coach Erik ten Hag currently short of options in the final third of the field.
Man City and Liverpool have both signed big-money strikers this summer in the shape of Erling Braut Haaland and Darwin Nunez, but the pair are also said to be long-term admirers of Pino.
The teenager featured in Spain's friendlies with Albania and Iceland earlier this year, scoring against the latter, but he was not involved in his country's UEFA Nations League matches in June due to an ankle problem.