Higuain, who told the media on the final day of the Primera Division season that he was going to leave Madrid in the summer, was reported to be on the verge of a £23millon move to Emirates Stadium.
However, during an interview with Univision, Perez said: "We don't want Higuain to leave.
"What's more no-one from Arsenal has come to us and made us any offers at all for him. There are no offers on the table."
Madrid have made two signings so far this summer, bringing defender Dani Carvajal and midfielder Isco to the Bernabeu from Bayer Leverkusen and Malaga respectively, but Perez remained tight-lipped on future transfers.
However, it has been reported Madrid will sign Spain Under-21 midfielder Asier Illaramendi from Real Sociedad in the coming days.
And although Perez did not confirm a move for the 23-year-old, he indicated Madrid were looking to sign a long-term replacement for Xabi Alonso, who will turn 32 in November and who suffered from a groin injury towards the end of the season which forced him to undergo surgery in June.
He admitted: "We are concerned about the state of Xabi Alonso. Defensive midfield is a very important position and we should be looking to strengthen there."
Uncertainty remains at Madrid over the long-term future of Cristiano Ronaldo, but Perez said he was calm about the situation.
He added: "Ronaldo wants to retire at Real Madrid, and we want him to retire here, just like Zidane and so many other great players did. You can be absolutely certain that Cristiano will retire at Real Madrid."