"He can be like a heavyweight Canelo Alvarez, really. He can be that good. He could have a middleweight's fighting style, but in a heavyweight frame."
Alvarez is widely regarded as one of the world's best boxers in any weight class, with his skill allowing him to compete in many divisions despite potential size disadvantages - having won world titles in four weight classes. While Parker can't achieve a similar level of decoration, Lee - a former middleweight world champion - believes he can be just as tough a talent for opponents to deal with.
On Sunday morning, Parker will look to show his continued improvement in his return to the ring against Joe Joyce for the WBO interim heavyweight title. This will be Parker's third bout under the watchful eyes of his new coach, and Lee said he had been impressed with the improvements Parker had made since his win over Derek Chisora last December.
The bout against Joyce is one that has many fans and pundits intrigued. While Parker has a clear advantage in his speed and movement, Joyce has a sizeable reach advantage and applies pressure by moving forward behind his jab. The 37-year-old comes into the fight undefeated in 14 professional bouts, while Parker comes in with a 30-2 record and the underdog tag.
Lee said it was a big test for both boxers, but that there was a clear path to victory for Parker.
"You can nullify everything in boxing, no matter what advantage your opponent has, with timing. Timing and positioning," Lee said.
"Everyone thinks boxing is in the hands, but boxing is really in the feet; it starts in the feet with footwork and positioning and feinting – all things that will hopefully win Joseph the fight."
A win this weekend will put Parker right back in line for a world title shot, looking to return to the lofty heights he reached in 2016 when he claimed the WBO strap.
But while there was plenty on the line against Joyce, Lee said he wanted his fighter to take a simple approach into the bout.
"You can get bogged down in visualising stuff and make fights more than what they are," he said.
"It's just a fight. It's no different to what Joseph's been doing every day in the gym. He's just got to go in there and perform; just box the way he has to always box. Nothing special, nothing extra. Doing what he does in the gym every day will be enough to win."