Lainez, 18, earned a move to La Liga at the start of 2019, but found it difficult to establish himself in the team previously coached by Quique Setien.
The winger made just three league starts following his transfer as Betis slipped to a 10th-placed finish, with Setien leaving at the end of the season to be replaced by Rubi.
According to reports in Mexico, America are keen to take their former gem back on loan for the coming season, which would ensure the regular first-team football he has found so sparse in Seville.
But Goal understands that a return to Distrito Federal is the last thing on the mind of the teenager, who is determined to break through in European football.
Sources close to the player revealed that Lainez made the decision to step up convinced that he has what it takes to succeed.
He therefore has no interest in coming back to Mexico after barely six months of La Liga under his belt, and foremost in his mind is the need to talk to new coach Rubi, establish his goals for the coming season and fulfil expectations with Betis.
Betis too are not willing to consider the sale or loan of a player they see as key to their future plans.
Club authorities have exhorted Lainez to be patient and wait calmly for his chance to shine, convinced as they are that he will grow to be a star at the Benito Villamarin.
Lainez is under contract until 2024 and in any case will not rush into any decision until he has spoken to the new man on the bench at Betis. For now, there is no prospect of a move away for the young star labelled one of Mexico's hottest prospects.
The Tabasco native made his debut for America at the tender age of 16, and went on to rack up more than 50 appearances for the Aguila, scoring five goals.
He has also been capped at senior level by Mexico and formed part of the Tricolor's Under-20 World Cup squad this summer, going out in the first round.