Having confirmed a second United bid for the former Arsenal midfielder ahead of his side's encounter with Yokohama F Marinos, it is believed Moyes would consider a third if Barcelona show no inclination to sell.
It would be a bid taking United beyond the ?30.75million it took to prise Dimitar Berbatov away from Tottenham in 2008.
Evidently, if Barcelona were to keep saying no, Moyes would have to look elsewhere.
However, given encouragement to believe Fabregas is open to the idea of returning to the Premier League, Moyes is not about to give up just yet.
"I think a point does come," said the Scot.
"But when you are interested in good players you want to give it every opportunity to materialise.
"I will hope things will continue to move forward.
"At this moment in time I can only tell you (executive vice-chairman) Ed Woodward is working hard to try and make the deals happen. We hope some of them will fall into place shortly."
Despite being linked with a host of big names, Moyes' only signing to date is Uruguay Under-20 defender Guillermo Varela.