Claude-Maurice has scored 17 league goals in his 55 appearances for Ligue 2 outfit Lorient.
Aliadiere knows the 21-year-old well having been at the French club while he came through the academy.
Claude-Maurice has been linked with a move to Arsenal and Aliadiere reckons it would be a smart piece of business.
“For the money that we talk about I think he’ll make it,” Aliadiere told football.london.
“It’s about taking a gamble now when other teams aren’t prepared to.
“The market has gone so crazy in the last few years. If you want a top level international it’s nothing cheaper than £40m.
“If they’ve only got £45m to spend you’ve got to shop differently, go a bit younger and sign players from second divisions. He’s a good player and has really good qualities.
“At a club like Arsenal that gives chances to young players it would be a good step for him.”
Aliadiere says Claude-Maurice has “amazing” technical ability but says he still has a lot to learn.
“I remember incredible quick feet, a technical player,” he continued.
“Technically he was amazing. The only thing – he was young at the time – was making the right decision, passing when you need to pass.
“He was dribbling all the time when I was there. But he’s a very sharp, skilful player.
“He didn’t always play the game in the way Lorient like to play the game, pass, movement. He was taking the ball and dribbling past everybody.
“He had qualities and was a really good young player but he had a lot to learn.
“He was very light, skinny, I wondered if it would take a bit of adaptation time if he came to the UK. But don’t get me wrong he has great potential.
“You don’t have to be massive, big and strong to play in the Premier League but you’ve got to be able to take a challenge and a tackle.”