Emery will take charge at Villa Park on November 1st after the club met his £5.25m release clause to bring the former Arsenal boss back to the Premier League, and Pochettino was the man that the Yellow Submarine wanted to replace him.
The former Tottenham Hotspur manager has been out of work since he was sacked by Paris Saint-Germain last summer after disappointing results in the Champions League and turmoil behind the scenes, although he has been linked to vacancies at Nice and Chelsea since.
Villa had contacted the Argentine to gauge his interest in a return to English football, however the 50-year-old made it clear that he was only interested in a role at a Champions League club.
Villarreal, who are competing in the Europa Conference League this season, were given the same answer, according to Spanish outlet Cadena Ser.
The club are seventh in La Liga and are reportedly set to appoint former Barcelona manager Quique Setien in the coming days.