Martinez wants to secure the 33-year-old on a permanent deal after his successful season-long loan from Manchester City last term.
"In a World Cup summer everything goes slow and everything happens at its own pace," said Martinez to the Liverpool Echo.
"Gareth is such a unique person, I have been so impressed and I think everyone at the club has taken to him.
"For us he would be an important player for the future but we respect him as a human being and we are going to accept whatever he decides and make sure whatever happens we are here to support him in every aspect.
"He has been a special player for us and we will try to give him an incentive to stay even though there is nothing you can say to a player who has experienced everything in the last 10 months.
"Football happiness is a major aspect any footballer chases and Gareth and Everton are a perfect fit and the way he has been performing shows he has that footballing happiness.
"We all know what Gareth brings and how important that is."
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