United have had two bids rejected for the 26-year-old despite the Spanish side repeatedly stating he is not for sale.
And amid speculation of a third bid for Fabregas, Zubizarreta told Spanish newspaper Sport that United have ended their pursuit of the former Arsenal midfielder.
Zubizarreta was quoted as saying: "Manchester United are interested in the player, but it's also true that they understand our position of not wanting to sell.
"They have renounced his signing. We aren't going to sell him."
Zubizarreta was also quoted by Barcelona's official website as saying: "He has a contract with us.
"We count on Cesc. I said that on the day of the presentation of Tito (Vilanova) and also with Tata (new coach Gerardo Martino).
"He's an extraordinary player who creates and finishes chances. We are delighted with him. He's the number four of Barca."