Mbappe has been heavily linked with La Liga side Madrid after the PSG star fuelled speculation over his future by hinting it could be time for a "new project".
However, Emery, who managed the fowrard for one season in France, revealed the desire Mbappe had to sign for Madrid during his time at PSG, which came to an end following the 2017-18 season.
"At some point, everyone pushed at PSG," Emery told Cadena SER. "I even talked to him and his father to stay.
"He wanted to choose Real Madrid, he also had a chance at Barcelona, but he wanted Madrid eyes closed.
"Among everybody we convinced him about the project in France and made him stay. We had to set money over the table, and that's what we did."
Mbappe joined PSG in a loan move from Monaco, which became permanent for a €180million fee, in August 2017.
Since then Mbappe has scored 59 goals in all competitions, netting 32 so far in Ligue 1 this season.
Emery, meanwhile, won seven titles – including the 2018 Ligue 1 trophy – in two years at PSG before he was replaced by Thomas Tuchel.
Arsenal will need to win that final in order to secure Champions League football next season.