Praise was heaped upon Carroll, 22, after he celebrated his first international goal in only his second start during Tuesday's 1-1 draw with Ghana at Wembley.
And Cole has likened the ex-Newcastle star's influence to that of former Chelsea colleague Drogba, insisting the ?35million January recruit has a very bright career ahead of him at Anfield.
Beware of the new Drog: Joe Cole reckons Andy Carroll can be even better than Chelsea star Didier Drogba
'He's very much like Didier Drogba,' said Cole, speaking to LFC Weekly.
'Andy's 22 - we all know what a cracking player Didier is, but he wasn'tplaying at this level at that age.
'There's still a lot of developing for Andy to do so he can get better and better.'
Carroll was the toast of England on Tuesday night, less than 24 hours after England boss Fabio Capello had ordered him to keep off the ale in pursuit of excellence.
Carrollscored his first international goal to fire Capello's team into a first-half lead but Ghana levelled the friendly in stoppage time with a brilliant solo effort from Asamoah Gyan.
'I'm here and I'm ready to score goals if I'm picked,' said Carroll, who was winning only his second England cap and starting only his third game since 10 weeks out injured.
'It's great to be playing again,' he added.
Handy Andy: England boss fabio Capello was delighted with Carroll's strike against Ghana
Capellotook the Liverpool centre-forward aside at the England campto discuss the reputation he has quickly acquired as a hard-drinking party animal and the Italian was reluctant to shower praise on the striker, even after his goalscoring display.
'Carrollscored a goal but needs more time to improve,' said the England manager.
'He can improve a lot. He's a really important player and it's important for the striker to score a goal.
'Iremember him before he suffered injury problems. He ran around a lot and would always fight. With the bigger players, it's impossible to improve really quickly, like Aaron Lennon and Jack Wilshere.'
Askedif Carroll would be allowed to celebrate his first England goal with a beer, Capello replied: 'This is a question for Kenny Dalglish.'
Red alert: Cole, who has struggled so far at Liverpool, is determined to become a hit on Merseyside
Cole, meanwhile, also saluted fellow Liverpool new boy Luis Suarez backing the Uruguay frontman to forge a fruitful attacking partnership with Carroll on Merseyside.
He added: 'Andy'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.'
Cole has endured a frustrating season so far since he signed for the Reds on a free transfer from Chelsea last summer but the 29-year-old one-time England star insists he is feels honoured to be at the club and has vowed to return to his best.
'I'm privileged to play for Liverpool Football Club and privileged to be a professional footballer,' said Cole, who has been hampered by injuries this term.
Joe Cole insists he still feels privileged to be at Liverpool Football Club despite a debut season of mixed fortunes.
Top man: Cole has praised Dalglish's new No 2 Steve Clarke for his role in Liverpool's revival
'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 downsand sometimes you just have to ride the rollercoaster. 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.'
While boss Kenny Dalglish has taken most of the plaudits for Liverpool's revival following the departure of Roy Hodgson in January, Cole believes the appointment of former Blues No 2 Steve Clarke has been equally key.
He added: 'I don't think you'll find a better coach around than Steve Clarke.
'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.'
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Explore more:People: Didier Drogba, Kenny Dalglish, Joe Cole, Roy Hodgson, Fabio Capello, Jack Wilshere, Aaron Lennon Places: Newcastle, Liverpool, United Kingdom, Ghana Organisations: Liverpool Football Club