Despite facing a fresh battle to win over the Kop, he is confident of making it - impressing in flashes as Liverpool began their North American tour with a 1-1 draw in Toronto on Saturday.
Cole told The Sun: "It was great to pull the shirt on again. I want to be part of this revival and I'm confident of fitting in.
"There is no point looking back, that's been and gone. When I came here I wanted to be part of the revival of this great club and nothing has changed in that respect.
"Everything I've done is in the bank but I want to write new chapters. I want to help make this great club successful.
"I have spoken with Brendan and I am looking forward to playing a part in it. I want to be part of this team and we are all in it together."