Bryan Oviedo has proved an impressive replacement in the absence of Baines, and Everton have won four and drawn one of their five matches without the England international.
Martinez said: "Leighton is getting really close. Depending how he goes in training over the next couple of days, 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."
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