United have been heavily linked with a move for the former Arsenal skipper recently after missing out on the signing of Thiago Alcantara, who opted to move to Bayern Munich.
And although the Red Devils have usually preferred to remain silent on transfer speculation, Moyes has now confirmed they have made a formal offer for Fabregas, although he was unable to reveal how far they were into negotiations with the La Liga giants.
"I couldn't tell you exactly," said Moyes, when asked what the lastest position is.
"The chief executive is dealing with it. Hopefully know more in the next few days."
Much has been made of the fact United are yet to sign any player of note since Moyes' arrival.
Having missed out on Thiago's signature, they continue to be linked with Everton pair Marouane Fellaini and Leighton Baines, in addition to a swoop for Tottenham's Gareth Bale, who it is said would cost upwards of £60million.
"As far as players we are looking to bring in are concerned, we are working hard to do that," Moyes said.
"We are trying very hard to make some additions.
"Hopefully there will be some good news in the not too distant future."
One player that has been said to be on his way out of Old Trafford is striker Wayne Rooney, whose future has been the subject of intense scrutiny in recent days, with Chelsea having already had one bid rejected.
It is anticipated it will not be long before the London club make another approach for the England striker, but Moyes insists United are not interested.
"The club's position has not changed," said Moyes, who has repeatedly stressed Rooney is not for sale.