The 27-year-old spent last season on loan at Juventus and is widely tipped to leave Anfield this summer, although it was thought that Fiorentina were leading the chase for his signature.
However, Milan are now on the hunt for a midfielder after Andrea Pirlo joined Juventus.
"He's a midfielder who has the characteristics we're looking for, so he could be of interest," Galliani said, before ruling out a move for Real Madrid midfielder Kaka.
"Kaka's wage is impossible for an Italian club due to the tax system," he said. "If someone comes in it will be a left central midfielder, not a striker."