Arsenal star Fabregas has long been linked with a return to Barca, the club where he learned his trade as a youngster before moving to the Gunners seven years ago and they are still hopeful of signing him this summer despite having a 35million euros offer for the Spain international rejected this week.
The 23-year-old is under contract to Arsenal until 2015 but last month reiterated his desire to head back to Barca and Xavi knows the club's blood runs through his international team-mate's veins.
"I would love him to come," he told Barca TV. "I have already told him so.
"He's a footballer made up of Barca DNA.
"I don't have any doubt that Cesc would triumph at Barca."