The Portuguese coash has been linked with a move to Spanish giants Real Madrid.
Real Madrid president Florentino Perez is reportedly keen to bring Mourinho to the Bernabeu to replace Manuel Pellegrini at the end of the season.
“Mourinho has a contract with Inter,” Moratti told Gazzetta dello Sport. “But besides this, I am certain that he will happily remain.”
Mourinho’s contract with Inter Milan expires in June 2011.