Deadline-day signing Oumar Niasse could make his Everton debut against West Brom on Saturday.
The striker, who signed from Lokomotiv Moscow last Monday for £13.5million, did not have clearance to face Newcastle last week and was left out of the squad for the weekend's 3-0 win over Stoke after only completing one full training session.
Niasse, a 25-year-old Senegal international, has not played a competitive game since December.
Asked if Niasse's debut could come against the Baggies, Martinez told evertontv: " It could. He had one full session with the team before the Stoke game but I thought it was probably a bit too early.
"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."
Meanwhile, Everton fans have voted nine-year-old George Shaw's half-time effort against Swansea as their goal of the month for January.
Shaw, who has cerebral palsy, was invited to the game by winger Gerard Deulofeu after a video of him playing football in the Spaniard's shirt went viral.
The youngster went onto the pitch at half-time and earned rapturous applause when he kicked the ball into the net.
Shaw received 86 per cent of the vote, with second place going to Ross Barkley's strike against Manchester City on six per cent.