The Chelsea midfielder was sent off for two yellow cards in a 1-0 qualifying win against Argentina in September 2025, meaning he is banned for their clash against the Ivory Coast in the United States on June 14.
The country's football federation have asked FIFA to wipe the suspension, according to Ecuadorian media reports.
"If Moi plays in the opener I will be happy, one always wants to have players who have that leadership and that presence," Beccacece told reporters.
"I always said that I thought it was possible to review the matter because I know how FIFA operate."
Beccacece said it would be the right decision to allow the 24-year-old to feature.
"I don't know how close or far it is... but hopefully (it will happen), because I think it's something that would be fair," continued the coach, who said the red card was an "injustice".
"It would be better, in these kind of situations, for the suspension to be served in the next qualifying campaign, to me it's completely logical and just common sense.
"Since I know how FIFA is, and the people around it are very football-minded, I always trusted this could happen - we'll see if that intuition comes true."
Ecuador, who had a strong South American qualifying campaign and finished second, have reached back-to-back World Cups.
They face 2022 semi-finalists Morocco in a friendly on Friday in Madrid, the first African side to reach a World Cup final four.
The Atlas Lions were controversially declared winners of the Africa Cup of Nations earlier this month despite losing the final 1-0 in January, after some players from opponents Senegal's team walked off after Morocco had been awarded a late penalty.
The Confederation of African Football said Senegal had to forfeit the match, with Senegal appealing against the decision before the Court of Arbitration for Sport.
In the wake of Morocco's January defeat coach Walid Regragui departed and was replaced by Mohamed Ouahbi, promoted from the Under-20 side after winning the World Cup at that level last year.
"He will give continuity to everything they've built up over time, because they've been doing things very well for quite a while now," added Beccacece.