Manchester United are believed to be tabling a third bid for Fabregas after having two offers rejected, although the Catalan side's sporting director Andoni Zubizarreta has indicated that the Barclays Premier League champions have now given up their pursuit of the former Arsenal captain.
Alves and his Barca team-mates hold the midfielder in a high regard, and the Brazil wing-back would be "delighted" if the 26-year-old chose to remain with the Primera Division champions.
In an extensive and outspoken interview with Catalan radio station Rac1, Alves spoke about Fabregas while also discussing Thiago Alcantara, who left Barcelona - his boyhood club - earlier this summer to join former coach Pep Guardiola at Bayern Munich.
"I think that Thiago hurried a little, but I like that attitude because the worst thing you can do is remain comfortable," Alves said of the 23-year-old.
However, he said it was wrong to compare Thiago to Fabregas, who left Barca for Arsenal aged 16 only to return aged 24 after seven campaigns with the Gunners.
Alves explained: "Cesc's is a different case. He has already left here once. He left the club, made a name for himself and then returned. He wasn't at his best at the end of last season but we were all the same.
"Football is a collective sport and you cannot look for scapegoats. If he decides to stay here, I'll be delighted to continue having him as a team-mate. The squad respects him a lot."
He added: "It's up to him what he does, but I think he can bring a lot to this side. The team needs players of Cesc's quality to win trophies."
Alves also risked the wrath of the Barcelona board by declaring his bewilderment at the club's decision to release Eric Abidal at the end of last season.
This year the French left-back made a full recovery from a liver transplant he underwent to fight cancer, making five appearances towards the end of the season.
But the 33-year-old was not offered an extension to his contract, which expired in June, and has since joined Monaco on a free transfer.
Alves has given up his traditional shirt number of two for next season and will instead wear the 22 that used to belong to Abidal.
"I have taken the number 22 shirt because I love Abidal and I do not understand his situation," the South American said.
"It was an unpleasant surprise to find out that he wouldn't be continuing with us. Given the huge efforts he made and for all that he has been through, they should have handed him a new deal.
"Barca showed that they are more than just a club for what they did to help him recover. For him to then leave leaves a bit of a bitter taste. Now he has to look to his own future. I am sure that he will continue to be an example to everyone around him where he is now."