He refuses to give up on his dream of making it at Anfield and insists he is a more mature player and person after 10 months in France at Lille.
Cole, 30, said: "I haven't had any conversations with Liverpool, but as it stands I'm back there for pre-season.
"When you don't know who the manager is going to be you cannot do much else really. I'm hoping to make it at Liverpool.
"My time at Lille has been extremely positive. I've moved back from the wing into a more central midfield role and I have thrived there.
"It's my best position, I was doing it at 19 for West Ham.
"The days of me running down the wing are over, I see my future in the middle now. It's where I can get my foot on the ball and get the best out of myself.
"Once a new manager is appointed then we'll see how it goes with him."