Out-of-favour midfielder insists the 22-year-old former Newcastle United forward is playing at better level than the Ivorian powerhouse was at the same age
The striker has spent most of his time on the sidelines since his £35 million move from Newcastle United, but his recovery from a groin injury has seen him regain his place in the England squad, scoring his first senior goal against Ghana on Tuesday night.
And Cole believes the 22-year-old is in a great position to follow in Drogba’s footsteps.
"He's very much like Didier Drogba," Cole told LFC Weekly.
"Andy's 22, we all know what a cracking player Didier is, but he wasn't playing at this level at that age.
"There's still a lot of developing for Andy to do so he can get better and better," he added.
"He's a good lad and I think you'd have been hard pressed to have found two better signings in January than Andy and Luis Suarez."
However, Cole himself has struggled to demonstrate the form which persuaded Liverpool to bring him to Anfield last summer, although he admits he is in a privileged position being a professional footballer.
"I'm privileged to play for Liverpool Football Club and privileged to be a professional footballer,” Cole added.
"The best thing you can do as a player is make sure that you don't take that for granted every day because it's a great lifestyle. There is nothing you would want to change.
"It's been a bit stop-start for me this season but football's all about ups and downs and sometimes you just have to ride the roller coaster. I just try to have a positive outlook and keep going.
"I'm enjoying my football at the moment and taking every day as it comes, making sure I work hard every day from the moment I come in to the moment I leave."
"I don't think you'll find a better coach around than Steve Clarke," he said.
"The lads really enjoy training and I am coming into work with a big smile on my face every day.
"I think all the lads are happy and results have picked up."