Regis is convinced there's much more to come from the on-loan Chelsea striker.
Regis told the Birmingham Mail: "I met Romelu after the Aston Villa game and he seems very grounded and clearly he's someone who wants to maximise his potential.
"If you've had a level of success you don't want to give it up. At the moment West Brom meet all of his needs. But the one thing you need if you're going to reach the very top is a propensity to grow 10-15 per cent every season as a footballer.
"Look at Ishmael Miller when he first came into the West Brom team - unfortunately he developed injuries and it held him back. He came with great potential but it was never fully fulfilled with West Brom.
"If you can grow by that extra percentage every year then you can become a great player.
"My game evolved but the peak of my strength, character, and, crucially, consistency came when I was 29-years-old when I won the FA Cup with Coventry in 1987.
"I had my best season in terms of goals in 1981-82 but I peaked five years later. Romelu Lukaku has that basis to build on. The challenge for him is to keep bettering himself."