The Premier League champions will make an improved third bid worth €41 million for the midfielder following the rejection of their latest offer.
But Pique is confident Fabregas will resist a move from Camp Nou as he worked so hard to rejoin the club he left at the age of 16.
"United are wasting their time," Pique is quoted as saying 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."
Moyes has publicly admitted United may be forced to accept defeat in their pursuit of Fabregas should they fail with a third bid, with the likes of Luka Modric, Yohan Cabaye and Marouane Fellaini all earmarked has potential back-up options.