The Everton frontman finds himself at the centre of transfer talk once more as his future continues to be called into question.
Leading sides across Europe have also been credited with holding an interest, with recent goings on at Goodison Park offering hope to Lukaku’s long list of suitors.
The burly frontman has opted against committing to a new contract and instead reiterated his desire to play at the very highest level – with Champions League competition having been talked up in the past.
Cole, a man who knows all about the art of goalscoring, is a big admirer of the 23-year-old and the qualities within his game.
He has, however, urged Lukaku to use former Liverpool frontman Suarez as an example of how to become the complete number nine.
"He’s young enough - he’s only 23," Cole told Football Focus.
"But he’s got a lot of work to do. When you talk about the best No 9s in the world, you look at Suarez.
"That is the level you’ve got to get to.
"He’s still learning the game. He’s got goals, he’s got power, he’s got everything.
"If you can marry that all together than in a couple of years he could be just that [world class]."
Lukaku has netted 22 times for Everton in all competitions this season, with 21 of those efforts enough to have him leading the race for the Premier League Golden Boot.