Alexander-Arnold produced a hit-and-miss display as the Reds sealed their first win of the season, but was forced off in the second half.
Joe Gomez took the right-back’s place in the 75th minute, with physios providing immediate treatment in the dugout.
Liverpool were able to take all three points at Anfield, but a setback for Alexander-Arnold left supporters worried ahead of the trip to Newcastle next week.
The 24-year-old was seen hobbling away at full-time with ice strapped his left ankle, but speaking in his post-match press conference Klopp gave a hopeful update.
“I hope so,” he said when asked if the player was OK.
“He told me now he got a kick. That’s pretty painful, but as far as he felt it, it didn’t twist or whatever – it was a kick.
“That’s why we changed then, but I hope he will be fine.”
Given his importance to not only the side, but the entire system it is built around, any injury for Alexander-Arnold would be a major blow.