Everton left-back Leighton Baines could return to action against Sunderland on December 26.
The England international has been out for the past month with a broken toe.
Everton have not lost in Baines’ absence, winning four and drawing one in the Barclays Premier League, and Bryan Oviedo has filled his position effectively.
Despite that, the return of Baines is likely to give a squad already flying high another lift.
Martinez said: “Leighton is getting really close. Depending how today and tomorrow go, he should be ready for Thursday, which is terrific news.
“Of course we have missed him. You can’t underestimate the quality of Leighton and his experience, know-how and what that represents.
“We have had an incredible replacement in Bryan Oviedo, he has been terrific.
“But you want players in good moments of form to be available.
“We are desperate to have Leighton Baines back and desperate for Bryan to be in that moment of form.
“We need to make sure we use that well for the good of the squad.”
Baines’ return to action ahead of the January transfer window could reignite speculation over his future.
The 29-year-old was heavily linked with Manchester United in the summer but Everton rebuffed offers.
Martinez is happy for the rumours to start up again – taking that as a compliment over his team’s form – but stresses he will be under no pressure to sell.
He said: “I hope we get more speculation. Now we are going to get Ross Barkley, I am sure, and Seamus Coleman.
“But that is a good sign. The problem is when you are in January and nobody speaks about your players.
“I am quite happy, speculation is welcome. We don’t have to sell. We are in a great position financially.
“That is what football should be about – people talking good about your players. It is a good message.”
Martinez expects striker Nikica Jelavic to overcome a minor hamstring problem before the Sunderland clash. Steven Pienaar and Sylvain Distin also suffered knocks in the weekend win at Swansea but should be fit.
Right-back Tony Hibbert, who has featured little in the past two seasons due to injuries, is also available after recovering from his latest knee problem.