United have already had two bids for Fabregas rejected with Barcelona consistently insisting the Spain international was not for sale.
A possible third United bid for Fabregas, 26, had been mooted but comments from Zubizarreta on Sunday suggest the Barclays Premier League champions have now decided to end their pursuit of the former Arsenal captain.
Zubizarreta was quoted as saying by Spanish newspaper Sport: "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, speaking in Israel where the Catalan giants are currently on tour, was also quoted as saying by Barcelona's official website: "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."