The 21-year-old's absence would be a big blow for the second-placed Scarlets as they look to narrow the 10-point gap at the top of the table and stop third-placed Munster and fourth-placed Glasgow from jumping above them in the standings.
Williams will be monitored over the next 48 hours but won't feature at Ravenhill unless he has fully recovered from the heavy knock that saw him leave the Liberty Stadium encounter midway through the second half.
The Scarlets could also be without new signing Joe Snyman as the South African is still struggling with a hip problem, while both George Earle and Gareth Davies are doubts due to rib damage and Aaron Shingler is dealing with a groin issue.
"Liam took a bump to the head and we've got to stick to the protocols on that," said Scarlets boss Simon Easterby.
"Some of the others are players have had bumps over the past couple of weeks and are trying to come back to fitness.
"It's a wait and see on a few of those. We're not able to give too much information, only because we don't know enough ourselves."
Meanwhile, Ulster are set to welcome back a whole host of big names after they slipped to their first PRO12 defeat of the season last time out.
Ulster boss Mark Anscombe made a raft of changes for the trip to Munster but is expected to select the likes of Rory Best, Chris Henry, Andrew Trimble, Darren Cave, Iain Henderson, John Afoa, Ruan Pienaar, Nick Williams, Paddy Jackson, Paddy Wallace and Jared Payne for the first game of the New Year.