Cole was sent out on loan to French club Lille last season as the Reds struggled in the Premier League under Kenny Dalglish, who was dismissed with the Northern Irishman taking his place this summer.
And, speaking on Liverpool's tour of the United States, Cole believes that Rodgers is the best man to help the club progress.
|BEST AND WORST NEW KITS
|Which Liverpool shirt was nominated?
"They also know a good manager, and you speak to anyone out here or back home and they know we have got a good manager.
"I can only see us going in one direction, but we have got to work hard to make sure that happens. It's not traditional for the club to change managers, but we need stability now. Everyone needs to be settled.
"I am 100 per cent sure that the right man is in the job. He is the best out there. The fans are intelligent. They know sixth, seventh and eighth in the last three seasons isn't good enough. But we are a work in progress now and we have got the right man in charge.
"All I can tell you about him is just how impressive he is - the lads have all been impressed with everything that he has done. Training has been good. He is just on the ball with everything.
"He is top-drawer. I can't tell you anymore than what you already know. It is a happy camp at the moment."
|BACK ON TRACK?|
|2/5||Liverpool are 2/5 with Bet365 to finish in the Premier League top six|
"I've got to win people over, I know that. People have asked me if I wondered what happened after I joined, but I am only looking forward," the attacking midfielder continued.
"Everything I have done in my career is in the bank. But I want to write new chapters. I want to be part of the revival of this great club and help make it successful.
"I have spoken with Brendan and as far as I am concerned, I am here, I am looking forward to the season and we will go from there."