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Fabregas, who won the World Cup last summer alongside eight Barcelona players, has long been linked with a move back to Catalonia, and he revealed before the tournament in South Africa that he would welcome the transfer but that the final decision rested with manager Arsene Wenger.
Asked if Fabregas would one day play for Barca, Xavi said: "I believe so. I do, because it's his wish to do it.
"I believe in life your dreams are above all, and his biggest dream is to be back at Barcelona. Arsenal have to find a financial agreement with Barcelona but Cesc's dream - and he said it publicly - is to play and triumph with Barcelona.
"He's triumphing at Arsenal where he is captain, and he's still very young, he still has many years in front of him.
"He would adapt very easily at Barcelona. In fact, he grew up here in camp Barca, he has Barca DNA, and I would like to see him here. But it not only depends on us or him - it also depends on the clubs."
Xavi, who was on the three-man shortlist for the FIFA Ballon d'Or along with team-mates Andres Iniesta and winner Lionel Messi, shrugged off talk that 23-year-old Fabregas would be his successor, instead insisting that the pair could replicate their international partnership at club level.
He said: "It depends on when he will be coming. It will depend on my age. I don't know. I feel very good here now, and if Cesc comes I think we can play perfectly together like we do in the national team.
"I always say the same thing: my game is made of associations, and the more players with my style and my qualities that I have around me, the better it is for me."