Mbappe is believed to be back on Los Blancos' transfer radar after admitting at the weekend that he will consider leaving PSG as he wants "more responsibility".
The French champions have ruled out a transfer ahead of next season but Emery, who is now in charge of Arsenal, says that the 20-year-old could easily have joined Madrid - or La Liga rivals Barcelona - 12 months ago.
"At some point, everyone pushed at PSG," he 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 has found the net 38 times in all competitions this term and leads the Ligue 1 scoring charts with 32 goals ahead of the final round of fixtures.