Pique: United wasting their time
United are understood have made a second bid of £30m plus add-ons for the 26-year-old former Arsenal midfielder after their initial offer was rejected.
However Pique, a former United defender, is quoted in The Sun as saying: "United are wasting their time. It took a long time for Cesc to get his dream move back home and he won't give it up.
"This is home. It is where his family is, and he is playing with his closest friends. He has told us he is happy and that he intends to stay with Barcelona."
Reports in Spain have claimed that Barcelona have rejected United's latest offer, but Moyes stated on Monday that he was waiting for a response and that chief executive Ed Woodward was dealing with the bid.
Speaking at a press conference in Yokohama, Moyes revealed: "As I understand it, Ed had a response (to the first offer). We have made a second offer but Ed is dealing with it rather than me."
So far, United have not made any new signings this summer, other than Uruguay Under-20 star Guillermo Varela and, whilst Moyes accepts there may come a time when he has to walk away from the deal, that position has not been reached yet.
"I think a point does come," said Moyes. "But when you are interested in good players you want to give it every opportunity to materialize.
"I will hope things will continue to move forward. At this moment in time I can only tell you Ed Woodward is working hard to try and make the deals happen. We hope some of them will fall into place shortly."
In addition to Fabregas, Moyes has also been linked with marquee signings Cristiano Ronaldo and Gareth Bale, plus Everton duo Leighton Baines and Marouane Fellaini, so far though, there have been no reinforcements and Moyes admitted he can understand why some fans are nervous.
"I can understand that feeling," he said. "But there have been quite a few changes. Other managers have changed their clubs too and everybody thought this might be the summer when transfers are done later in the month.
"That was always the thought I had when I came into the club. You have to remember I only started on July 1, so in truth I have only been in the job three weeks at this present time."
Moyes has admitted signing a new midfielder is his priority ahead of the new season, although Barcelona have warned the Premier League champions off Fabregas, who rejoined Barca in 2011 following eight years at Arsenal.
Following United's 5-1 win over the A-League All Stars on Saturday, Robin van Persie expressed his desire to be reunited with Fabregas, having played alongside the midfielder for Arsenal.
Van Persie said: "Of course, he's a great player."
United goalkeeper David de Gea has also recently confirmed he would relish the chance to play with his fellow Spaniard at Old Trafford.
De Gea told the Daily Mail: "He is a great player, very skilful, knows how to win things and you always want those type of players in your team."
However, Barcelona vice-president Josep Maria Bartomeu confirmed last week, prior to coach Tito Vilanova's resignation, that Fabregas is not for sale.
Bartomeu was quoted by Spanish daily Sport on Friday: "Barcelona can assure you we will not entertain any offers for Cesc. It is totally ruled out, he's not for sale."