Garbutt has played 10 times for the Toffees this term and is considered to be one of the club’s brightest prospects, but the left-back could well depart this summer.
Garbutt's contract expires at the end of the campaign and the 22-year-old has made no decision as yet on where his future lies.
"He's been part of a very successful story, as another academy graduate who has been given a chance in the first team," Martinez said.
"He is now in a situation where he wants to think. It is not 100% what he wants to do and that is something we have to respect.
"Obviously, we want to keep him, but the player needs to be fully on board and we should find out very soon."
To lose Garbutt at this stage of his career would be a major blow for Everton, as they have invested so much time in improving and developing him.
The defender has been one of the side's most exciting youngsters for some time and it seems that he is on the verge of a first-team breakthrough.
It may be that Garbutt feels his future is best served elsewhere, though, as competition for places is fierce at Goodison Park.
Garbutt needs to dislodge England international Leighton Baines if he is to get a spot in the starting line-up, and that would be a tough test for any promising youngster.