The 46-year-old has been out of work since leaving Bury in 2017. He joined the Gigg Lane club after leaving Ayrshire following exactly one year in charge of the Rugby Park side.
Hibs are said to be on the search for a new manager after Neil Lennon and assistant Garry Parker were suspended by the club on Friday.
Clark was able to successfully save Kilmarnock from relegation three months after joining when his side defeated Falkirk in the play-off final.
Though he signed an astonishing 24 players the following season, most of whom failed to make an impact at the club, he was able to uncover a couple of gems in Souleymane Coulibaly and Jordan Jones.
He told the Daily Record: “I’d be very interested to sit down and talk with them and hopefully I’ll get that chance.
“I thoroughly enjoyed my time up there. I liked the openness and honesty of everyone involved in the game up there, the players, the staff, the supporters, it was just genuine honesty.
“It brought a freshness back and I had a great time, in hindsight I probably took the opportunity to move on to quickly.
“Once I was inside the game up there I felt it had been undervalued, especially down south, and hadn’t been getting the respect it deserved. There’s lots of talented players as well and high-profile managers up their now, I just think it was getting a disservice.
“There’s a lot of big games to look forward to particularly when you’re working in that environment.”