The French side paid around £7m to sign the 24-year-old during the summer transfer window, bringing his six-year spell at the Bernabeu to an end.
Reports in the Spanish press recently suggested that Zinedine Zidane was keen to bring the Dominican Republic international back to the club, having scored nine goals in 12 appearances for Lyon since joining.
However, Aulas is adamant that, contrary to press speculation, Madrid do not possess the right to re-sign the player at the end of the season.
"It is false there is no special buy-back clause for Real!" he posted on Twitter.
Mariano made 14 league and cup appearances for Madrid last season, scoring his only La Liga goal in the 3-2 win over Deportivo La Coruna in December.