The Premier League champions have had two bids rejected this summer and were rumoured to be lining up a third offer.
However, Zubizarreta has said that the Catalan giants' unwillingness to sell has forced United manager David Moyes to admit defeat.
"Manchester United are interested in the player, but it's also true that they understand our position of not wanting to sell," Sky Sports News quotes him as saying. "They have renounced his signing.
"We aren't going to sell him. We count on Cesc. He's an extraordinary player who creates and finishes chances. We are delighted with him. He's the number four of Barca."
Fabregas played in the Blaugrana's 8-0 demolition of Santos on Saturday.