The right-back suffered a calf injury in the 1-1 draw with Manchester City on Sunday.
And multiple reports in the UK have revealed Alexander-Arnold underwent a scan on Monday to assess the damage.
Speaking after the draw with City, manager Jurgen Klopp was annoyed with the Premier League's scheduling.
"The boys are on the edge," he said. "No team on a Wednesday night should have the 12:30 kick-off on Saturday.
"Sunday - no problem. Not the 12:30 because that is a complete killer. You wake up and play football. This is the recovery phase.
"The Premier League has to change. Sky, BT, you - everyone has to talk to each other.
"You want good football? Give the boys a few hours more rest."