Garner came through the Manchester United academy but was sold to Everton in the summer of 2022.
The young midfielder has gradually come into his own at Everton and has emerged as a key player under Sean Dyche.
Garner was highly regarded at Manchester United but was ultimately allowed to move on by Erik ten Hag last year.
However, he drew comparisons with Carrick when he was at Old Trafford and Mulvey admitted that those are appropriate.
The Manchester United academy coach believes there are similarities to their game but stressed that Garner still has to realise his potential and achieve what the former midfielder did during his career.
Mulvey told The Athletic: “Michael Carrick was around the first team at the time and a lot of people made comparisons.
“He’s got a long way to go yet, but that’s the potential he’s got.
“There are a lot of similarities in the way Michael used to break the game up and be a good passer.
!He had an amazing career and hopefully, Jimmy does the same.
“The world’s his oyster, really.”
Garner scored in Everton’s recent win against Bournemouth at Goodison Park just ahead of the international break.
