In a speech to fans at Rugby Park after Kilmarnock defeated Rangers 2-1 to finish third in the standings and secure a Europa League spot, Clarke appeared to drop a hint about his next role as Alex McLeish's successor.
"When I came here, we had a disconnect between the support, the board, and the players and I said together we're stronger," Clarke, who took charge of Kilmarnock in Oct. 2017, said.
"In my time at Kilmarnock, I'm sorry I didn't win you a trophy but I stand here in front of three stands of Kilmarnock supporters -- that's my trophy."
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McLeish was sacked last month after 12 games in charge following Scotland's disappointing start to their Euro 2020 qualification campaign.
The Scottish FA is expected to name a new manager ahead of their squad announcement for next month's qualifying matches against Cyprus and Belgium.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Pritha Sarkar)
