The 28-year-old Toffees winger has been in fine form and scored on Saturday for the third game in a row in all competitions.
He has 21 England caps, but has not made an international appearance since February 2013.
Roy Hodgson was watching Saturday’s match from the stands, and when asked afterwards if he thought Lennon had any chance of making England’s Euro 2016 squad, Martinez said: “I get the opportunity to work with Aaron day in, day out, and he is such an important player.
“We all know the quality he brings — the pace, the one-v-one ability, the work-rate, the understanding — and that experience he has is invaluable.
“There are other players in that position, but I think he is showing he can be of incredible value to any squad, and clearly for his national team, he could be a real help.”
Lennon scored the third goal of a first-half blitz from Everton in which Romelu Lukaku and Ireland’s Seamus Coleman also netted.
Lukaku converted an early penalty awarded for a foul by Jack Butland on Tom Cleverley, making it 20 goals in all competitions in 2015-16, the second successive season he has reached that mark.
Coleman showed great desire for his goal, beating his marker Erik Pieters and connect with Cleverley’s corner to nod past Butland.
Martinez confirmed Lukaku had played through the pain after being forced off by a back injury in Wednesday’s win over Newcastle.
“He has had injury problems but he doesn’t want to miss games,” Martinez said.
“You run out of compliments you can pay to Rom.
“He lives for the game. He is an old-fashioned footballer, at the age of only 22. He just comes in and wants to work on his game constantly.
“He is a goalscorer who is obsessed with finishing quality.”
It was also Stoke’s third straight league defeat by that scoreline, having recently exited both domestic cup competitions as well, and their commendable season looks like it may be petering out.
They have been hampered by injuries at the back, but after another sloppy performance defence-wise, boss Mark Hughes has stressed the need for specific work up front.
“We are a little bit threadbare at the back, but sometimes you have to help yourselves defensively as well, and that means the whole team has to contribute,” he said.
“We have an opportunity this week to get on the training pitch and do specific work.
“We’ll make sure we get down to the fundamentals, the basics, and get back on track.”
Butland, Johnson, Wollscheid, Muniesa, Pieters, Imbula, Whelan, Shaqiri (Odemwingie 62), Afellay (Ireland 62), Arnautovic (Joselu 76), Diouf.
Bardsley, Crouch, Krkic, Haugaard.
Robles, Coleman, Jagielka, Funes Mori, Oviedo, McCarthy (Osman 90), Barry, Lennon, Barkley (Mirallas 87), Cleverley, Lukaku (Kone 76).
Baines, Deulofeu, Pienaar, Stanek.