David Moyes' side have had two bids rejected for Fabregas, and yesterday Barcelona's sporting director Andoni Zubizarreta revealed that representatives from the Barclays Premier League champions had informed him they had given up on their pursuit of the 26-year-old.
Speaking during the club's two-day visit to Israel, Zubizarreta declared: "They have told us that they understand our position and have confirmed that they're withdrawing from their attempts to sign Cesc."
The Barcelona squad arrived in Thailand this morning and although Fabregas has yet to make any comment on his future since the bids were made, the message from his team-mates was clear.
"Being as good a player as he is, it's normal that clubs will make offers for him, but he has always told me that he wants to stay at Barcelona and triumph here," Pique told a press conference, quoted in Sport.
The defender added: "That's always been his dream and I'm very happy that he's staying. I think he's never been in doubt."
Iniesta reiterated Pique's comments, underlining the importance of Fabregas
to the team's future.
"He is indispensable, like everyone else in the squad," said the midfielder.
"He's fundamental to this team, he has performed very well for us so far and is going to do the same again next season."
Barcelona have made just one signing this summer, bringing Neymar to the Nou Camp from Santos for 57million euros.
Yesterday Zubizarreta hinted that the club were looking to sign a centre-back, but Pique warned that it was not easy to find a player who would be able to adapt seamlessly to the team's style of play.
He said: "It is difficult to find the profile of player Barca need because our way of playing is unique. Experience tells us that it's not easy to find a centre-back for Barcelona."