The former Gunners star is being let go as a free agent by La Liga champions Barcelona and Kenny Dalglish is interested in snapping him up, according to Metro.
The report states that Anfield boss Dalglish is keeping an eye on his situation after Barcelona agreed to cancel the player’s contract for a pay off.
Hleb left Arsenal in the summer 2008 and the Catalan club eventually paid €17million for his signature.
The Belarussian did not enjoy a successful time at Barca, however, and was sent out on loan to various clubs, including then Barclays Premier League side Birmingham City.
The 30-year-old was supposed to spend the entirety of this season on loan at Bundesliga side Wolfsburg, but he returned to Cataluña six months early due to form and fitness restricting his involvement.
Barca are desperate to get his reported £90,000-a-week salary off their wage bill as there is no likelihood he will play for the club again.
The report suggest they are now willing to compromise and let him go in a free and Hleb apparently wants to move back to the Barclays Premier League where he had the best years of his career.
Queens Park Rangers have also been credited with an interest in the former Stuttgart man, whose contract runs out at the end of the current season.