Niasse joined the Toffees on deadline day from Lokomotiv Moscow, and there were suggestions that he could have made his first appearance against Stoke City last weekend.
However, the attacker missed out on that match, as he was only able to train once with his new teammates before they travelled to the Britannia Stadium.
After having another week to settle in, Martinez now feels that Niasse is ready to feature, though, and the Spanish boss has hinted that his new addition could play a part when the Toffees take on West Bromwich Albion on Saturday.
“He had one full session with the team before the Stoke game but I thought it was probably a bit too early [to involve him],” he said.
“This week has been completely different, he has had a really good working period and all he needs is some good solid work before he can compete in the team.
“The Premier League is a competition that you have to be ready in order to have an impact.
“It is important he gets the time and the understanding he needs but, at the same time, I have seen he is desperate to be involved.”
Niasse faces a fight to win a place in Everton’s team over the coming weeks, given the fact the Merseyside outfit have won each of their last three games 3-0.
Niasse is able to play out wide, or as a central striker, but his chances of breaking into the starting line-up look limited, as things stand.
The likes of Gerard Deulofeu and Aaron Lennon have been in great form in recent weeks, while Romelu Lukaku seems certain to retain his place as Everton’s main striker.