The Red Devils are keen to bring the 26-year-old Barcelona playmaker to Old Trafford and have lodged a bid in the region of £26m for the midfielder.
The offer is understood to have been rejected by the La Liga champions, but executive vice-chairman Ed Woodward has left United’s pre-season tour to continue negotiations.
And when asked if he had received any official contact back from Barcelona, Moyes told a news conference: “I couldn’t tell you exactly.
“I’m in contact with the executive vice chairman [Woodward], who has been dealing with it just now.
“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.”
Speaking earlier this week, Barcelona boss Tito Vilanova insisted that former Arsenal captain Fàbregas is keen to stay at Camp Nou rather than move back to the Premier League.
“There have been offers for him from other clubs, but I spoke with Cesc and he told me that he was still determined to stay here and be successful, so I’m not worried,” said Vilanova.
“He doesn’t want to go to other teams for money reasons or playing time. He knows there is competition for places here, but his decision is to stay. I am relaxed about the situation.
“It is a good sign that the club gets offers for our players. It shows we have players other teams want. But Fàbregas wants to stay.”
Fàbregas has scored 29 goals and made 32 assists in 96 appearances for Barcelona after completing a £35m move to Camp Nou from Arsenal back in August 2011.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news