The manager revealed United has made a second bid for the Spain international after its first bid was met with an insistence that the former Arsenal playmaker was not for sale.
Last week United revealed an opening offer for the playmaker of 30 million euros had been made to Barca on Monday. However, Barca vice president Josep Maria Bartomeu insisted on Friday that the 26-year-old is not for sale.
The latest offer is reported to consist of 35m euros plus add ons, while the former Arsenal midfielder is contracted to the Blaugrana until 2016.
The United manager told the club's official website: "My understanding is that Ed [Woodward, United's executive vice chairman] had a response and he spoke with them. I think we made a second offer but Ed is dealing with that personally, rather than me."
Moyes went on to say that he wanted to give the deal every chance.
"When you're interested in good players you want to give it every opportunity to materialize and I'll do that," he said.
"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."
Long-serving midfielder Paul Scholes retired at the end of last season, and the Red Devils' options in the middle of the park going into the new season were further depleted following the news that Darren Fletcher will miss the start of the campaign as he recovers from surgery.
The Red Devils had previously targeted Spain's under-21 European Championship winning Thiago Alcantara, but the 22-year-old opted to join former Blaugrana manager Pep Guardiola at Bayern Munich, while the former Everton manager has also been linked with a move for the Toffees' Marouane Fellaini.