Robertson has returned to Merseyside for treatment after a nasty fall under Spain goalkeeper Unai Simon left him with a suspected dislocated shoulder.
The severity of his injury remains to be seen, with potential surgery likely ruling him out for the remainder of the year, though the hope is that his layoff will be much shorter.
After scans and allowing the issue to settle, Liverpool will be able to determine how long their left-back is expected out.
As it stands, Clarke is unsure if he will have his captain available for Scotland’s two games against Georgia on November 16 and Norway on November 19.
“As always with injured players, we send them back to their club; Andy’s gone back to Liverpool,” he told reporters on Monday.
“Liverpool will deal with his injury. Obviously it’s a shoulder issue and Liverpool will deal with it.
“If he’s fit for next month, it’s great. If he’s not fit for next month then hopefully he’ll be fit as soon as possible for his club.”
It is far from the most optimistic diagnosis, and it suggests that, with Clarke to be kept up to date as Robertson’s national team manager, no conclusion has been drawn yet.
The reality is that Jurgen Klopp will be planning for an extended period without Robertson, with Kostas Tsimikas poised to start the Merseyside derby instead.
Youngster Luke Chambers is also available in reserve, while Joe Gomez could potentially shift over to left-back if required.
Another injury blow has emerged from the Scotland camp, too, with Ben Doak unable to feature for their U21s against Malta on Tuesday.
The Scottish FA have confirmed that Doak will miss the U21 Euro qualifier due to injury, though no specifics on the issue have been reported as of yet.
Like Robertson, the teenager will return to Liverpool for assessment, with fingers crossed he is passed fit for the coming games – as a likely starter against Bournemouth in the League Cup fourth round.
