The national team boss is among the favourites to take over at Parkhead following the departure of Neil Lennon, along with current interim boss John Kennedy, Manchester City youth coach Enzo Maresca and former Bournemouth manager Eddie Howe.
Clarke was put on the spot during a Q&A with children from Edinburgh-based Team United, which supports young people with autism and helps them overcome social barriers, when he was asked about his plans after this summer's delayed 2020 Euros.
He responded: "After the Euros I will go on a big holiday. It is going to be very tiring then we will decide what happens.
"But I have a contract with the Scottish FA up until December 2022 and hopefully I can take the team to the World Cup finals in Qatar in 2022 as well, that would be great and then maybe I can think about club football."
The former West Brom, Reading and Kilmarnock boss added: "When you have been in football as long as me, you tend not to look too far ahead.
"I look forward to the games in March and if we can win all of them we can concentrate on the Euros after that and we will see what happens."
Clarke is currently preparing for this month's World Cup qualifiers against Austria, Israel and the Faroe Islands, before turning his attention to Scotland s first appearance in a major tournament in 23 years.
The former St Mirren, Chelsea and Scotland defender insists there is still potential for new faces to make his squad ahead of this summer.
He said: "I don't think there will be too many surprises for the Euros. The players who did the hard work and got us qualified deserve first chance.
"But before we get to the Euros we have three games in March so there might be one or two surprises in that squad.
"I need to pick a bigger squad because we have three games in a week, a very short period of time, and maybe one or two in that squad might force themselves into my plans for the summer."
One certainty for the squad is Manchester United midfielder Scott McTominay, who has played in defence at international level and was described by Clarke as the best he has worked with in his time as Scotland boss.
He said: "The reason I go with Scott McTominay is that I asked him to play out of position, in a position he was a little bit unfamiliar with, and I thought the way that he played in the games was outstanding."
One of the youngsters also asked Clarke if he supported a football team and the 57-year-old replied: "Yes. The team who I played over 400 games for, Chelsea. That's my team."
During lockdown, over 70 children from Team United have been using the Scottish FA's European Legends legacy project as a means to stay motivated and connected.
Clarke joined the kids to celebrate 100 days to go until Euro 2020 kicks-off in 12 host cities across Europe.