The 28-year-old's last match was for the Toffees on May 16 at the end of his loan spell but having rejoined permanently on deadline day for a fee of £4.5million he is keen to get started
Fellow deadline day signing Ramiro Funes Mori is also likely to be in the squad despite him not returning to Finch Farm until Thursday after international duty with Argentina
"I'm not worried about his physical state and he needs to play games now to sharpen up his play," said Martinez on Lennon.
"He's refreshed and is in a great position
He knows the football club inside out and is desperate to get back to Goodison.
"From that point of view, I expect Aaron to be involved one way or another at the weekend."
Lennon, who scored two goals in 14 appearances on loan, is confident he can hit the ground running.
"I haven't played pre-season games but I've trained a lot and I feel really good," he told evertonfc.tv.
"I'm in good condition so once I get the game time in I don't see why I won't be straight up to speed."
Martinez is still missing left-back Leighton Baines but has been boosted by the news Brendan Galloway, who has stood in this season, has returned to fitness after a knee problem while he also has the option of playing Funes Mori on the left while Bryan Oviedo's recovery from a knee injury will be assessed over the next two days.
"With Bryan, it's difficult
I don't know if the weekend is too early or not - we'll find out over the next 48 hours," added the manager.
"I think Brendan is progressing well and should be available, in the same way that Ramiro Funes Mori could become available.
"The way I see Ramiro, he is able to play in any of those positions when he is needed, so in that respect it is about assessing how he feels
It's a long journey coming back on Thursday morning and we'll assess that from a physical point of view."
Midfielder James McCarthy is expected to be available after playing two matches for the Republic of Ireland despite a minor knee problem.
"We are going to see how James McCarthy comes back because he had a little bit of a problem in his tendon in his knee before he joined the international setup but he got through the games really well so in that respect we are quite positive," said Martinez.
Source : PA
Source: PA