Sturridge, 21, enjoyed a highly-productive loan spell at Bolton during the second half of the 2010-11 campaign, firing eight goals in 12 appearances.
But Cole says he is unsurprised by the former Manchester City striker's progress and has backed him to emulate that success at Stamford Bridge - if he is given the chance.
"I saw Daniel Sturridge recently and look at what he has done at Bolton,'' Cole told Chelsea's official website. "I knew what he could do. I've seen him in training and he's honestly one of the hardest players I've ever had to mark. His movement is unreal.
"Hopefully when he comes back next season he'll see more opportunities and bang goals in for us like he has done for Bolton.''
However, reports continue to place doubt over Drogba's Chelsea future while Sturridge's from at Bolton cannot be ignored by whoever is chosen to replace manager Carlo Ancelotti.
Ancelotti was sacked after the Blues finished second in the Premier League and fell at the quarter-final stage of the Champions League. Cole, however, believes the club should not be too discouraged by what they achieved last term.
"At the start of the season we played some good football, some sexy football to be fair,'' Cole said. "Blackpool at home in that first half was special, but it's been a tough season.
"When we had that crazy, not even a blip, an unheard of period for any team, everyone wrote us off and rightly so. But give us credit for coming back and it's an achievement to come second in the Premier League. That said, though, we feel as though we should be winning and we want to win, but second is not bad in this league.''
Cole, Chelsea's Players' Player of the Year, expects to continue for at least three more years as he manages a troublesome left ankle injury.
"I don't feel 30. We train with a lot of young players and they make you feel young. I feel good,'' he said. "I feel healthy and fit, so I hope to keep going for a few more years, though it's hard to say how long.
"I do have a bad ankle and it's not something which just goes away so I have to manage it and take it season by season. But if I look now and say how I feel, I know I've definitely got three years.''