The striker missed last Saturday's 1-0 win over Chelsea but is set to return against the Hammers after the bruised bone in his knee improved.
Martinez told evertontv: "He should have a very good opportunity to be involved on Saturday. He has still got a bit of bruising in his bone - he got a knock in training - but we hope over the next 48 hours he will be available to be with the side."
The Goodison boss also had positive news on Darron Gibson, with the Republic of Ireland midfielder in line to return from his own knee problem some time soon.
"We need Darron fit. Darron is a special player and he brings something different to the side," said Martinez.
"He is progressing really well. I would say that from a medical point of view, he is very close to being fit. Now it's the match fitness he needs to get.
"That could take a bit of time and we need to adapt to how the knee reacts to work.
"But we are really happy to see him ready and really close to being able to be involved and be in the squad."
Martinez also hinted that Steven Pienaar's injury could clear up sooner than some reports have claimed.
"With Stevie, we need to assess him week to week," he added. "When you get the sort of soft tissue injury he has, you never really know.
"I do feel that Stevie will react well to treatment. He is a very fit boy and I do feel that he will probably be back quicker than anyone expects."
A second summer from Martinez's old club Wigan, Antolin Alcaraz, who is still awaiting an Everton debut after undergoing surgery on a groin problem, is also nearing a first taste of action.
Martinez said: "After the surgery Antolin had in his groin, now he is still recovering.
"We need to make sure that we get him the right program and the medical department is working really well with Antolin.
"We need to help him to get through this period. We hope that he is going to be fully fit very soon."