Lukaku arrived at Stamford Bridge in 2011 from Anderlecht when he was a teenager, but he failed to make his mark at Chelsea.
The 28-year-old Belgian star made only 15 appearances for the Premier League club and was loaned out for spells at West Brom and Everton.
Lukaku left Chelsea in 2014 for Everton and enjoyed success with the club before moving to Manchester United in 2017.
The Belgium international has been with current side Inter Milan since 2019 and was in excellent goalscoring form for the Serie A champions last season.
Lukaku scored an impressive 30 times in 44 appearances as he helped fire Inter to their first Italian league title in 11 years.
Cole, who enjoyed a successful eight years at Chelsea, rates the Inter striker's development since his days with the Blues.
The 40-year-old former left-back claimed that Lukaku faced stiff competition in establishing himself as the main striker at Chelsea ahead of Blues legend Didier Drogba.
However, Cole added that Drogba was a "kind of father figure who used to help [Lukaku] in terms of developing his technique and understanding of movement."
When asked about Lukaku's woes at Chelsea, the ex-England international told ITV Sport: "He joined as a kid, he joined as a 17-year-old.
"[He was] a raw talent, his game understanding was not great. Didier Drogba was his kind of father figure who used to help him in terms of developing his technique and understanding of movement.
"And then I think the two loans really gave him that self-belief that he was good enough. Yes, he was still young but he still had a point to prove.
"I think no-one kind of respected him at Chelsea, in terms of the fans. When he did play, was he going to be the top striker for Chelsea? He had Didier Drogba in front of him.
"For him to go on loan and prove to himself, he definitely came back with that self-belief, that courage, and now his performances have been second to none, he's been quality."
Lukaku has carried over his fine Inter form on the international stage as he scored a brace against Russia in Belgium's opening Euro 2020 win last Saturday.
Featured Image Credit: PA/ITV
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