The 21-year-old left-back has been on the books of the Merseyside outfit since 2009, when he joined them from Championship club Leeds United.
The youngster’s current contract with Everton runs out at the end of the season, and Martinez wants him to sign a new deal.
“I want him to stay at Everton but in the same way you cannot force players to stay if they don’t want to stay,” the Spaniard told The Guardian.
“I hope that we can solve it in the summer and work together in that respect. You need to accept what the player feels as well.”
Garbutt has been able to make just three appearances in the Premier League so far this season, creating four chances in the process.
The England Under-21 international has a pass accuracy of 80%, and has won four headers and four tackles.
The main reason for the youngster’s lack of playing time is the presence of Leighton Baines, who remains one of the best left-backs in the Premier League.
The England international may be 30 years of age, but he remains as mobile and good as ever.
For Garbutt to further his career, he needs to play regularly; and to play regularly, he needs to leave Everton. It is as simple as that.