Bale, who joined Real from Tottenham for a world-record fee thought to be around £85 million in September 2013, has been linked with a return to the Premier League.
United are said to be keen to lure the Wales international to Old Trafford, but Perez is adamant the 25-year-old will not be leaving the Santiago Bernabeu.
Perez told Marca: "We haven't received any offer for Gareth Bale, not from Manchester United or any other club.
"We'll never listen to any offer for Bale regardless of how important it is."
Bale has enjoyed great success since making the move to the Spanish capital, forming an intimidating attacking trio with Cristiano Ronaldo and Karim Benzema.
The former Southampton man was on target in extra time for Real as they came from behind to beat city rivals Atletico Madrid 4-1 in the UEFA Champions League final in May and win Europe's premier club competition for a 10th time.
