It has been suggested that Spain international Fabregas is once again figuring prominently on the transfer wish list of Manchester United.
The Premier League outfit pursued the former Arsenal midfielder for long periods in 2013, only to see him remain at the Nou Camp.
Fabregas has offered no indication that he is looking to secure a return to English football any time soon, and Barca maintain that he remains an important figure in their plans.
President Josep Maria Bartomeu told Onda Cero: "We don't want to sell players.
"Barca do not want to sell Fabregas or any other players that may appear to be on the market."
Among those also generating plenty of speculation ahead of the re-opening of the transfer window are versatile Argentine Mascherano and long-serving playmaker Xavi.
Neither, though, are going anywhere according to Bartomeu.
He added: "Mascherano is a key player on the field, he stays at Barca.
"Xavi's contract ends in 2016 and he has two more years with the club. Coaches rely on experience for the future, and he has been at the club for 16 years."
Barcelona have also been linked with a number of possible incomings, with a transfer embargo postponed on appeal.
Atletico Madrid midfielder Koke is said to be interesting several clubs, but Bartomeu does not expect the talented 22-year-old to become available.
He said: "Koke is a spectacular player that all teams would like, but Atletico had a magnificent season and they will want to have another."
Bartomeu added that Atletico forward Arda Turn is 'not to be observed', but hinted that a move for Paris Saint-Germain defender Marquinhos could be a possibility.
"The club is looking for a successor to Carles Puyol," he said. "There was a Barca before Puyol and there will be one after. Marquinhos is a good player but we are in talks with various teams."