The two clubs became embroiled in a war of words last summer when Real publicly courted the 24-year-old, with United manager Sir Alex Ferguson vowing never to sell "that mob" a "virus".
Perez, recently returned for a second stint as president at the Bernabeu, has said he would still like to sign world player of the year Ronaldo - but not at the risk of upsetting the Premier League title winners.
"If one day there is a chance of [Ronaldo] playing for Real Madrid, that would be an honour for us," Perez, who also wants to sign Kaka from AC Milan, told The Times.
"But if I had to choose between the friendship with Manchester United and the signing of Ronaldo, I would choose the friendship.
"Plus, I have never said that Cristiano will arrive in June. That is an arrogant and false statement."
He continued: "I shall be talking with [United manager Sir Alex] Ferguson and [chief executive] David Gill to build bridges.
"If we sign Kaka from Milan, I can assure you that we will still have a very good relationship with [vice president Adriano] Galliani."