The 30-year-old is set to return to Anfield in pre-season following the conclusion of his loan with French side Lille and believes he can thrive in a central role
The former Chelsea star appeared to have no future at Anfield after being marginalised by boss Kenny Dalglish, who took the reins from Roy Hodgson last January.
However, following the Scot's sacking, the 30-year old now has a chance to impress any new manager and has set his sights on staying with the club.
“I haven’t had any conversations with Liverpool, but as it stands I’m back there for pre-season,” Cole told The Sun.
“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,” he added.
The 56-times capped England international netted nine goals during his time in Ligue 1, helping Rudi Garcia’s side qualify for the Champions League for a second consecutive season.
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He has regularly featured in a central attacking role for the French giants this term, a position which he believes he will occupy for the rest of his career.
He said, “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.”
Cole, who was left out of Roy Hodgson’s England squad for Euro 2012 last week, also refuses to give up on his international career.
He said: “England has gone in a different direction and there’s nothing I can do about that. But I still believe I could play in two years’ time at the World Cup in Brazil.
“I won’t give up. I’m going away for a couple of weeks but then I’ll start training by myself to keep ticking over in case I’m in the Olympic squad. That would be brilliant.”