The Liga giants have already knocked back a £25.9m opening offer from the Red Devils, although Moyes has since confirmed that the club have returned with an improved bid.
"I think we made a second offer but Ed [United executive vice-chairman Woodward] is dealing with that personally, rather than me," Moyes told reporters in Tokyo.
"When you're interested in good players you want to give it every opportunity to materialise and I'll do that. I hope things can continue and move forward.
"At this moment in time I can only tell you that Ed Woodward is working hard trying to make the deals happen. We can only hope that some of them fall into place shortly."
Twenty six goals from last summer's headline signing Robin van Persie helped catapult United to the 2012-13 title, so would a potential Fabregas arrival at Old Trafford have a similar effect?