Van Persie took over the Gunners captaincy when Fabregas departed for European champions Barcelona in the summer. Now, the Spain midfielder expects his former club to do everything within their power to tie Van Persie down to a new long-term contract.
"I don't know if they will keep him," Fabregas is reported as saying in the English press. "It is his decision. At his age, if he wants to move, it will be his last chance and it he wants to stay he will stay and retire at Arsenal.
"We will see what he decides but he's been very loyal to Arsenal for a few years. He is a key player, the fans love him. For me, he is the role model of Arsenal, the star player and they cannot afford to lose him.
"He is having an amazing season and hopefully he will be fit for the whole season. Unfortunately, when I was there, he never enjoyed a whole season and it was one of the things I regret a little bit.
"I hope he can keep going like that. Could he come to Barcelona? He would fit in anywhere but I'm an Arsenal fan and I want him to stay at Arsenal."
Van Persie's future is as yet unknown as contract talks with Arsenal have stalled, with the club confirming they will not resume until closer to the end of the Premier League season.
For Fabregas, though, he is pleased to have made the move away from the Emirates as he continues to enjoy his time at Barcelona, the club of his youth.
"I know that some people thought I wouldn't get in the team," he said. "Maybe they didn't believe in me too much. Things are going very well. I'm smiling, scoring and playing. I'm with my friends every day. For me, it is like a dream at the moment.
"I'm playing more than I expected so I'm very happy. I want to win trophies and so far I've won two [the Spanish Super Cup and European Super Cup] and we go to the Intercontinental Cup in Japan [in December] and that would be a very nice thing to win as well.
"I speak to the boys at Arsenal. Arsenal gave me everything and I will never forget that. I will try to come and see people when we have a Christmas break in Spain. It will always be a special club.
"The fans have always been amazing to me. I have only amazing words to say about them. It was a shame that they started the season so badly because now they are back to winning ways and doing well."