The Metro suggests that the Premier League clubs are interested in signing the former Arsenal midfielder, who has recently returned to the Catalan club after a disappointing loan spell with Bundesliga side Wolfsburg.
Hleb has failed to make an impact at the Spanish giants and manager Pep Guardiola is rumoured to be keen to release the Belarus international.
The 30-year-old recently admitted that he regretted leaving Arsenal in a £15m deal in 2008.
Hleb said: "I've given away the best years of my career. And I hold no-one responsible for it."
Barcelona are also willing to release Hleb on a free transfer.