While re-affirming the Premier League champions' stance that striker Wayne Rooney is not for sale, Moyes also revealed that United are waiting to hear back from the Spanish giants over the prospect of signing former Arsenal captain Fabregas.
United have submitted a big-money bid, with club chief executive Ed Woodward flying back to England from their Asian tour to work on the deal.
Speaking at a press conference in Australia ahead of their pre-season clash with the A-League All-Stars, Moyes said he was hopeful that the Fabregas situation could be resolved soon - with possible movements over the weekend.
"I'm in contact with the executive vice chairman who has been dealing with it just now," Moyes said. "I'll hopefully know a little more in the next day or so.
"It's the middle of the night back in England right now so I may have a bit more information in the next day or so about how it's going.
"We're trying very hard to make some additions to the squad and hopefully there'll be some good news in the not too distant future."
Moyes was also adamant that United's stance on Rooney remains the same, amid speculation Chelsea are putting together an improved bid for the England striker.
"The club's position on Wayne Rooney is there's no change to that," he added.
For now, the Scotsman's current focus is working his squad through his first pre-season at the club, as they build towards the start of the Premier League season next month.
Moyes confirmed striker Robin van Persie, who only joined up with the side in Sydney on Monday, would play some part in the game with the All-Stars at ANZ Stadium.
"We'll probably only use Robin in the second half. We've over-trained him this week to make sure he builds up his fitness," Moyes said of the Dutchman.
"We've not come with a massive squad so that means everyone will play some time.
"Well, that's the plan. I wanted all the players to get 90 minutes.
"We've enjoyed having Robin here. He met up with us when we arrived in Sydney.
"He was a massively important part of Manchester United last season and I'm hoping he'll have just as big an influence this season."