Van Persie has put off new contract talks at Arsenal until the summer.
Asked if Van Persie was good enough to join him at the Nou Camp, Fabregas said: "He would fit in at any club but I'm an Arsenal fan and I want him to stay.
"We will see what he decides but he's been very loyal to Arsenal.
"For me, he is the role model of Arsenal, the star player and they cannot afford to lose him. He is a key player, the fans love him.
"He is having an amazing season. Hopefully he will be fit for the whole season."