The Belarus international completed his protracted move to the Camp Nou last week for a fee reported to be in the region of ?15million (£11.9million).
Hleb had made no secret of his desire to quit the bright lights of London, but, in a thinly-veiled swipe at Arsenal, questioned why he, Gilberto Silva and Mathieu Flamini were allowed to leave.
The 27-year-old also said he would be delighted to see Spain star Fabregas and unsettled striker Adebayor join him in La Liga.
"These are fantastic players, Adebayor and Cesc," said Hleb. "Every team would like to keep these players. For me it would be fantastic if they came to Barcelona.
"Those players would bring good energy and power to this club. For Barcelona, it would be fantastic, and for me personally as well, if they leave."
He added: "Sometimes I think that Arsenal do not want to keep this team, not give something more."