Garbutt's contract at Everton expires in the near future, but Martinez insists that he is hoping to keep the youngster on Merseyside.
Most Everton supporters are hoping that Garbutt stays too, but rumours of an impending exit were strengthened when he was left out of the Toffees' starting line-up at the weekend.
Martinez opted to start Brendan Galloway instead of Garbutt against West Ham United, but the Spanish boss insists that this wasn't an indication that the 21-year-old's time at the club is up.
“Garbutt is a very successful story. Last year, he was in the Under-21s and we put forward a two-year programme," he said.
“Sometimes in football you don’t get the chance to get through but he’s played 10 games for the first team and has had a fantastic season for us.
"Luke Garbutt and Brendan Galloway are very different players."
If Garbutt does leave Everton it would be a major disappointment as he has been touted as Leighton Baines' long-term replacement.
The 21-year-old has impressed during his breakthrough season and to lose him at such an early stage of his career would be a frustration.
If Garbutt's contract does expire it is unlikely that he will be without a club for long, as he has the potential to make it to the very top of the game.