The Premier League champions had made an opening offer of €30 million for the Spain international, after Thiago opted to join up with former boss Pep Guardiola at Bayern Munich rather than move to Old Trafford.
|14/1||Wayne Rooney is 14/1 with bet365 to be the Premier League's top scorer
"As far as players are concerned, we’re looking to bring some in and we’re working hard to do that," Moyes told reporters.
"We’re trying very hard to make some additions to the squad and hopefully we’ll have some good news in the not too distance future.
"I couldn’t tell you exactly where we are with that [Fabregas]. I’m in contact with the executive vice-chairman [Ed 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."
Moyes also reiterated the club's stance that wantaway striker Wayne Rooney, who was subject to a bid from Chelsea this week, is not for sale.
"The club’s position on Wayne Rooney is there’s no change to that."