The 22-year-old arrived at Goodison Park from Iraklis Thessaloniki in 2011 and has since made only 24 appearances for the club, scoring three goals.
The Greek frontman failed to make a single league appearance for Everton during the 2013-14 campaign, but made two starts during a loan spell at Championship side Blackpool.
And Spaniard Martinez believes Vellios will benefit from a move away from Goodison Park.
"I think it's been a disappointing season for himself but he's always had a terrific attitude and always a real desire to try to work hard for the team," Martinez told evertontv.
"He's probably in a position now where, at a very young age still, he needs a new challenge and a new environment to show what he can do.
"We wish him well and I'm sure every Evertonian will follow me with that."
