If he can do that, impatient Real fans and management will be prepared to overlook the methods by which it may be achieved as success in the Champions League has become their Holy Grail.
Real won Europe's top club competition three times in six years between 1998 and 2002, made the semi-finals in 2003 and the quarters the year after, but have failed to progress beyond the last 16 since.
Last season's surprise exit to Olympique Lyon, their sixth successive defeat in the first knockout round, sealed Manuel Pellegrini's fate, while failure to reach the final at their own Santiago Bernabeu stadium was particularly galling.
Barca went one better to finish three points ahead on the final day of the season, with their home and away victories over Real in the clasicos' the difference between the two giants.
Mourinho, of course, out-manoeuvred Pep Guardiola's side to knock them out of the Champions League at the semi-final stage, and he will be expected to do something similar next season when the sides meet in the league.
Mourinho is likely to want more control over who is signed and will fiercely resist any kind of interference in team affairs from Perez's right-hand man Jorge Valdano and sports director Miguel Pardeza.
The Portuguese is the 10th coach hired in eight years since Vicente del Bosque led them to their last European triumph in 2002, and he has to please the suits upstairs as well as a demanding fan base, many of whom are suspicious of Mourinho's reputation for being a defensive coach.
Keeping a Galactico like Kaka on the bench, for example, will test the patience of Real's marketing men and the fans, but they will perhaps forgive him if he leads them to next year's Champions League final.
