The Blues had an £9million bid for Babel rejected earlier this month after the Dutchman himself reportedly turned it down.
But following another spat with manager Rafa Benitez, the 23-year-old is prepared to leave Anfield.
“Birmingham is still a possibility,” Babel’s agent, Winnie Haatrecht, told The Sun.
“It would be simpler for Ryan to continue in the Premier League, a competition he knows well.
“We’re actually studying an offer.”
