The Scotland boss faced the media on Tuesday following his squad announcement for the upcoming World Cup qualifiers against Austria, Israel and Faroe Islands.
Clarke is among the favourites to replace Neil Lennon at Parkhead but has vowed he will remain in charge of Scotland for this summer’s delayed 2020 European Championships after guiding the nation to its first major finals since 1998.
But when quizzed over his future beyond the tournament, and the links to Celtic, the 57-year-old left the door open by refusing to shoot down the speculation, admitting there are no guarantees he will still be with the national team.
Clarke said: “I don’t think it’s my job to knock anything on the head because I’m the Scotland manager. I told you on the steps in Serbia after the game and straight to your faces that I’d be here for Euro 2020. I said I would still be the manager of Scotland.
“If you can tell me that I’ll still be the manager of Scotland come December 2022 in Qatar I’ll be delighted with that as well.
“People can speculate all they want but it’s not my job to get involved in speculation. I can’t knock anything on the head.
“Why would anybody say they don’t want anything? Why would I do that? I could be somewhere else in the summer, I don’t know what’s going to happen.
“Did you know this time last year that we were going to be stuck in the house all this time by a pandemic? Nobody knows what’s going to happen so I don’t think it’s fair that you always say I’ve got to knock it on the head. I didn’t start the speculation.
“I’m delighted and proud to be the manager of Scotland.”
Asked if he was flattered to be linked with the Celtic job, Clarke added: “Flattery comes because my players have been fantastic, my staff have been fantastic, and we’ve had a little bit of success. Without the success you don’t get the speculation. That’s the way I see it.”