The Manchester United boss remains eager to bring in new faces and is hopeful that a deal can be reached for the Barcelona midfielder.
The reigning Premier League champion had made an offer of 30 million euros for the Spain international after transfer target Thiago opted to join up with former boss Pep Guardiola at Bayern Munich rather than move to Old Trafford.
Despite Barcelona boss Tito Vilanova's insistence that Fabregas wants to stay at Camp Nou, Moyes has revealed that United is pressing ahead with its pursuit of the former Arsenal star.
"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 distant 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," Moyes said.