The former West Ham United and Chelsea player has made just eight appearances this season and only four of those have come as first-team starts.
Brendan Rodgers inherited Cole from previous regimes when the Anfield boss arrived this summer and earlier this season he questioned whether the 31-year-old was justifying a reported salary of £90,000-a-week.
Speculation is now suggesting the ex-England international will be moved on in January to make way for Chelsea's Daniel Sturridge and Blackpool's Tom Ince.
But fresh from goals against West Ham and Young Boys, Cole said in the Daily Mirror: "All I'm doing is giving my all in training every day, and trying to keep my place in the squad when we play Villa. That's all I can do.
"It has been difficult recently but I have scored in my last two appearances and I want to keep the sequence going if I can. And when I'm called upon, I will do the best job I can."
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