The Northern Irishman left Swansea City to take Kenny Dalglish's role at Anfield recently and returning midfielder Cole, who spent last season in France with Lille, is looking forward to playing under the former Chelsea coach.
"I know him from my Chelsea days when he was there and I can't see anything other than positive things," he told the club's official website.
"When I was hearing about Liverpool looking at certain managers, I was praying it was going to be Brendan - not just because he's not an unknown for me and I know his philosophy on football, but I think for the club the owners have made the right choice. He has just impressed everyone so much since he's been here.
"It's been a breath of fresh air. A new manager always brings a lift, but the gaffer has come in and really impressed everyone.
"You talk to anyone - any of the players to the ground staff to the guys on the door - everyone is really impressed with him.
"The manager has made it clear, it's not just the players it's everyone in and around the club. For us to get the results we want, we've all got to come together."