The Red Devils have made two offers for Fabregas, the second of which is a reported £30 million. Both have been rejected by Barcelona, and president Sandro Rosell has apparently written to United to insist that the player is not for sale.
The press in the UK report that United are now weighing up whether to make a third and final offer in the region of £35m.
Pique, however, suggests that David Moyes would be better off looking elsewhere.
"United are wasting their time," Pique said, in quotes picked up by The Sun.
"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."
The BBC have quoted a Barcelona source as saying: “Fabregas is not for sale. The President has been very clear with Man United.”
The 26-year-old is thought to be Moyes's top target as he looks for a marquee signing to herald a new era at Old Trafford. Even he, however, admits there will come a point when United have to admit defeat.
"I think a point does come," said the Scot. "But when you are interested in good players you want to give it every opportunity to materialise. I will hope things will continue to move forward.
"At this moment in time I can only tell you (executive vice-chairman) Ed Woodward is working hard to try and make the deals happen. We hope some of them will fall into place shortly."
Despite being linked with a host of big names, Moyes' only signing to date is Uruguay U20 defender Guillermo Varela.
With Thiago Alcantara opting to join former Barcelona boss Pep Guardiola at Bayern Munich and links with Cristiano Ronaldo, Gareth Bale, Everton duo Leighton Baines and Marouane Fellaini, plus Newcastle's Yohan Cabaye as yet failing to bear fruit, some United supporters are starting to get anxious.
"I can understand that feeling," Moyes 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."
Nevertheless, it is hardly an ideal situation for United.
Woodward returned to Europe from Australia on "urgent transfer business" last Thursday.