The Greek forward has been with the club since 2011, when he moved from Iraklis, but has since made just two Premier League starts for the club.
He has slipped even further down the pecking order this season and has not made a single appearance.
Martinez still believes Vellios can have an impact at Goodison Park, but first he needs to overcome his reluctance to go out on loan.
"Long term I see him with great potential, but in the short term he needs minutes," he told the Liverpool Echo.
"Going out on loan is something we're going to assess, but going down the line it comes down to if the player is open to do that, and in the past it doesn't seem like that was something he was ready to consider.
"Tolis has got the potential to be a terrific number nine. He's good in the air, strong, powerful and has good link up play and mobility. He's at the stage now where he needs to be playing 90 minutes.
"Now is the time he needs to start developing his decision making over 90 minutes. If he does that I could see him having a role in the first team.
"We'll give it time but he needs games. We've seen his potential, and in pre-season he's made sure everyone is aware of that. Hopefully we can get the next step in his development right."
