The former Arsenal midfielder has been struggling to find his best form in the opening weeks of the new season, and has received his fair share of criticism in recent weeks.
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Nevertheless, Pique is confident that Fabregas will come good in the end, and play a key role for Barca again.
"Cesc is feeling very well. He put in a great performance against Saudi Arabia the other day," Pique told Cadena Ser.
"Every player goes through highs and lows throughout their career. We have played only three league games, yet people are already speculating that he will leave in the winter.
"There's a clear lack of patience in the footballing world if you ask me. He looks very calm to me and I am confident that he will eventually have a spectacular season.
"One of his handicaps is that Barca paid a lot of money for him. That brings a lot of pressure with it. And when things are going less smooth than expected, people start to speculate and start rumours.
"I don't like it, but that's the way football seems to work. This time it's Cesc who's affected by it."
Fabregas returned to Barcelona from Arsenal in the summer of 2011, and made 28 Liga appearances last term.