Clarke takes his squad to Denmark for vital Group F qualifier in Copenhagen on Wednesday, before returning to Glasgow for a match against Moldova on Saturday. Scotland then travel to Vienna on Tuesday, September 7 to play Austria.
However, the national team’s preparations have been hampered by the news that midfielder John McGinn is following Covid-19 protocols after testing positive and will miss the Denmark match, while Celtic manager Ange Postecoglou does not expect winger James Forrest and left-back Greg Taylor to be available.
Rangers right-back Nathan Patterson was also a surprise omission from the Old Firm game as the club deal with a Covid-19 outbreak.
Furthermore, Arsenal defender Kieran Tierney will need to be assessed after picking up an injury in the 5-0 defeat by Manchester City on Saturday, while Southampton’s Stuart Armstrong has withdrawn.
Self-isolating Aston Villa midfielder McGinn missed his team's Premier League draw against Brentford on Saturday and later revealed he returned a positive Covid test last Monday.
"All the Scotland boys are close so it's been difficult keeping this quiet and not telling them I won't be playing," McGinn said. "That's been strange but I'll be the same as everyone else on Wednesday – I'll be a Scotland fan.
"I'm not naive enough to think I'll just come back and be absolutely flying but I'll do whatever it takes to make sure I'm ready for the Moldova game (on Saturday) if and when I get a negative test next week."
The 26-year-old later added on Twitter that he had "no symptoms" and was "feeling fine".
Forrest and Taylor missed Celtic's 1-0 cinch Premiership defeat by Old Firm rivals Rangers at Ibrox on Sunday and when Postecoglou was asked after the match if Forrest would be available for his country and said: "I would say unlikely."
Then, quizzed about Taylor, who has a shoulder problem, the Australian replied: "Again, I would say unlikely, but I will leave that to the medical teams. Greg wasn't ready today so I think unlikely.
"He [Forrest] was close. We had him in the squad. He trained [on Saturday] and he just didn't feel 100 per cent.
"It is a long season and we didn't want to unnecessarily throw him in there.
"I was hopeful. As of [Sunday] morning he was still in the squad and we had to pull him out."
Motherwell right-back Stephen O'Donnell could be a doubt after missing his side's 1-0 win over Dundee on Saturday through illness, the third match in a row he has sat out.
There was better news elsewhere for Clarke as two strikers returned from illness to score for their teams.
Lyndon Dykes came off the bench to net his third goal of the season in QPR's 2-0 victory over Coventry, while Kevin Nisbet struck in Hibernian's 2-0 win against Livingston.
Clarke will now need to decide whether to go to his stand-by list and bring players into the camp, who are due to train for the first time on Monday before flying out to Copenhagen on Tuesday afternoon.