The Germany international limped off 10 minutes before Dejan Lovren‘s added-time winner in the 4-3 victory after falling awkwardly in a goalmouth scramble.
He had a scan on Friday and the details are expected to be known in the next 24 hours.
“We will have to see what the scan shows,” Can said.
“I twisted my ankle. I hope it’s not too bad but it’s too early to say.”
The 22-year-old is suspended for Sunday’s trip to Bournemouth but would have expected to return from the ban for Wednesday’s Merseyside derby at Anfield.
That has been put in doubt and his absence, following a week after fellow midfielder Jordan Henderson‘s season was ended by a knee injury, will be a blow after another impressive performance against Dortmund.
“We want to win that trophy,” he added.
“There are still good teams left in it and the semi-final won’t be easy but we just have to keep believing in ourselves.
“Going through is a big achievement because Dortmund are such a good team.
“This is a big result and this is for everyone, it’s for the whole city.
“It was unbelievable. I’ve never played in an atmosphere like that before.
“Everyone believed – that’s why we won the game – and now we need to continue like this.”