A house in Liverpool is only worth about £3-£4k so it's hardly a big commitment or signal of intent....
In all seriousness though, it's a very weak story. Why would be buy a house in a city where he is unlikely to be returning to? If he didn't even buy a house in Liverpool when he was playing for us, is it likely that he's bought one there even though he's playing in London, and possibly newcastle next season? You'd have to presume that BR has told him his future is most defnitely at anfield.