Sporting director Lars Ricken chose his words carefully after Saturday's 2-0 win over Hamburg, unwilling to commit to anything before the club knows the full extent of the damage.
"Depending on how serious the injury actually turns out to be, we will shape our next steps accordingly. What is certain, though, is that we won't be planning anything over the next three days," Ricken said.
Borussia Dortmund had prised Konstantelias away from PAOK Thessaloniki only weeks ago for a fee in the region of €26m, and the Greek playmaker delivered an outstanding first appearance in black and yellow, scoring his side's second goal before being forced off in the 52nd minute.
He twisted his knee in an innocuous-looking duel with Hamburg's Bakery Jatta - there was no contact from the Hamburg player - and Dortmund now fear the worst, with a cruciate ligament tear suspected pending further examination.
The uncertainty around Konstantelias appears to have already had a knock-on effect elsewhere in the squad. Fabio Silva, who had been expected to leave before the transfer deadline with interest from Spanish and Dutch clubs including Real Betis, was an unused substitute throughout the Hamburg win and looked visibly frustrated at full time - a sign, many suspect, that Dortmund are now reluctant to let attacking cover leave the club with Konstantelias's fitness in doubt.
Ricken's caution over the "next three days" is widely read as buying time to assess Konstantelias properly before finalising any decision on Silva's future, with the transfer window closing on Tuesday leaving Dortmund little margin to change course either way.
Head coach Niko Kovač was similarly guarded but struggled to hide his concern.
"What makes me very sad is that Giannis got injured and that we may be talking about something more serious. Our team doctor didn't sound too optimistic," he said after the match.
Konstantelias had looked every inch the marquee signing before his withdrawal, combining fluently with fellow Greek recruit Konstantinos Karetsas in a lively opening 45 minutes, his goal deflecting in off Hamburg defender Sebastiaan Bornauw.
Formal scans are expected in the coming days to confirm the diagnosis, with Dortmund bracing for news that could rule the 23-year-old out for a significant part of the season.