Hleb moved to Barca this summer after three seasons at the Gunners.
"We get on very well on and off the pitch. For me he is like a brother. We call each other a lot to talk about things," Hleb said in El Mundo Deportivo.
"He tells me he misses me at Arsenal and, without wanting to detract from anyone, I would love it if he came to Barca to be a part of all this.
"I will keep boring him until he changes his mind. If in the end he listens to me, I think it would be great for Barcelona."