As exclusively revealed by Goal, United have been preparing a final £35m for the Spain midfielder in their attempts to prise him away from Camp Nou.
Moyes, however, insists that no decision has been made on United's next move, while also emphasising the quality already on show at Old Trafford.
|1/2||Cesc Fabregas is 1/2 with BetVictor to sign for Manchester United
"Undoubtedly we hope to add to it and I'm quite confident we'll do that ... certainly before the window shuts."
Barcelona recently told Manchester United that the 26-year-old is "not for sale at any price".
"United's interest for Cesc Fabregas is obvious - he's a great player but it does not bother us," Barca vice-president Josep Maria Bartomeu told reporters. "It does not matter what they offer us, we are not selling him.
"If there was a higher offer, would we accept it? No. We're proud that a club like that wants one of our players."
Meanwhile, new Blaugrana boss Gerardo Martino also expressed his desire to keep Fabregas with the La Liga champions.
"I won't get involved in the economic interests of the club but, [if it's up to me], we will have him [Cesc] here," the Argentine boss declared.