The Red Devils have made an opening offer of 30m euros for the 26-year-old, but his coach insists the Spain midfielder wants to prove himself at Camp Nou.
The English club has made an opening offer of 30 million euros for the former Arsenal captain, who has failed to hold down a regular first-team place since returning to Camp Nou.
Having already seen Thiago depart to rejoin former boss Pep Guardiola at Bayern Munich, Barcelona is keen to avoid losing another world-class La Masia graduate this summer.
Vilanova is confident Fabregas is still motivated by the prospect of proving himself at his boyhood club and has no thoughts of returning to the Premier League.
"I am aware that we have received offers from other teams. I talked with him and he told me he wants to stay," the manager told reporters.
"Cesc doesn't contemplate the possibility of going to another club. He knows that the competition here is great. His dream is to succeed here."
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