The 23-year-old Argentina international has been linked with a move away from the club due to a lack of first-team chances.
AC Milan, Fiorentina and Boca Juniors have all been linked with the midfielder.
Pellegrini said: “Gago remains an important player and I have no intention of letting him leave during the winter transfer window.
“I’m sure that he will recover his place soon and help Real.”
