Hleb left the Gunners for the Catalan giants in the summer of 2008, but endured a difficult season at the Nou Camp where first team appearances were significantly limited.
And the midfielder has warned Fabregas against making any rash decision to quit Emirates Stadium.
"I stay in touch with Cesc a lot and it's hard for me to judge what he should do," the Belarussian said.
"He and Gael Clichy are both very good players who must make their own decisions about their future. But I would advise them to stay.”
Hleb has spent the whole season on loan at former club Stuttgart - the club that initially led him to Arsenal - and is expected to return to Spain in the summer to forge a permanent move elsewhere.
The Belarus international remains confident that his former side Arsenal can be more competitive in the Premier League next season, and hopes that stars such as Fabregas remain with the Gunners in their bid for success.
"It didn't work out for Arsenal this season but, if Arsene Wenger keeps the side together, they can really go far next year. They play great football," he added.
"It's partly a question of experience and next season Arsenal will have more of it if everyone stays."
"All things being equal, I think they have a very good chance of the title next season."
By Joe Brewin
