The former Chelsea star moved to Anfield in 2010, but failed to make an impact and was loaned out.
The 30-year-old spent last season with French outfit Lille, but with Rodgers' appointment he now looks to have a chance of rebuilding his Liverpool career.
"I know him from my Chelsea days when he was there and I can't see anything other than positive things," said Cole.
"When I heard 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 the owners have made the right choice for the club - 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."
Cole is looking forward to seeing Rodgers' footballing philosophy in operation.
"Sometimes in English football people automatically think you need to be aggressive. But look at Spain - no-one works harder than them," he added.
"I firmly believe in that and think it's now the way forward in football. We've seen how successful Spain and Barcelona are.
"The top teams get the ball down and play and move, and that's what we are going to try and implement here.
"But it takes time to change things, and great things take time. It's going to be a building process.
"As long as we stick together and try to do what the manager wants us to do, this club will move steadily forward again."
Cole was included in Liverpool's squad which departed for a pre-season tour of North America on Monday.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.