The former Arsenal man has been linked with a return to the Premier League following a difficult season with the Catalans last term, with Manchester United believed to be keen to take him to Old Trafford so he can join up with his former Gunners team-mate Robin van Persie.
But, during an interview with Movistar, Fabregas insisted: "People talk a lot but the truth is that no-one has spoken with me.
"I want to triumph in Barcelona, that club is my home and I always dreamed of playing there, so I will try and succeed there as long as I can."
Next year Fabregas will be playing alongside new signing Neymar, who joined Barcelona earlier this month.
The Spaniard believes the Brazilian has the capabilities to light up the Nou Camp but said he must be given time to bed in after moving club, league and country.
"Neymar will need time to adapt because he is coming from a completely different type of football from what he will find here. We need to help him settle in and grow so that he can give us great nights," said Fabregas.
He also dismissed talk that there could be a clash of egos between Neymar and Leo Messi.
"The egos are very controlled in the team," he said. "Messi has won the Ballon d'Or four times and is probably the best player of all time but when you see him every morning he doesn't seem like it."
Although Neymar cost Barcelona an estimated 57million euros, Fabregas raised alarm at the possibility of the club's biggest rivals Real Madrid spending 100million to buy Gareth Bale from Tottenham.
"For me spending 100million on Gareth Bale is foolish, I don't know how any club could spend that amount of money in these circumstances," he said.
"He is a great player with all the right attributes, but we will have to see if Madrid sign him and if he can perform there."