The 51-year-old, who has been in charge of the capital club since Lennon’s shock departure last month, confirmed Saturday’s 3-1 Scottish Cup fifth round victory over Raith Rovers would be his last match at the helm.
May will oversee first-team training on Monday alongside coach Grant Murray before returning to his previous role as head of academy coaching.
Michael Appleton is the front-runner for the head coach’s job after impressing the Hibs hierarchy during two rounds of interviews and, while unsure who the chosen man will be, May said an appointment should be confirmed on “Tuesday or Wednesday”.
May said: “That will be my last game and I am delighted to go out on a win. The new man is coming in and at least we are in the quarter-final.
“I have been told this was my last game and that the new man will come - I was told about five minutes before kick-off. I won’t be in charge for the Hamilton game.
“I don’t have a clue who they’ve got. They just thanked me and Grant for what we’ve done and the new man should be announced some time this week.
“I know Grant and I will take training on Monday as normal and maybe Tuesday or Wednesday the new man will be announced. It will be exciting and challenging because the new man will maybe put a different stamp on what he wants.”
If, as expected, Appleton is appointed, he arrives at Easter Road with Hibs just one game away from a trip to Hampden after they booked their place in the last eight.
Mark McNulty’s maiden goal for the club added to strikes from Daryl Horgan and Vykintas Slivka as the hosts saw off John McGlynn’s League One outfit. Euan Murray did net a late consolation with a fine header.
Raith boss McGlynn was proud of his side’s efforts after they refused to crumble, despite slipping three goals behind their Premiership opponents.
The former Hearts manager said: “Did the best team win? Yes, definitely. We needed Hibs to have an off-day, which they didn’t. Hibs played very well. And we needed to stay in the game and I’m proud of the players that at 2-0 down we didn’t ship four or five. We didn’t want that to happen.
“At 3-0 it’s difficult, but we didn’t crumble and stuck together. We showed good spirit and got a goal back and, if we had got it back to 3-2, it would have been interesting - very interesting. But I’m reasonably proud of how we played.”