The 21-year-old has become a key part of Klopp's side, playing in 13 of Liverpool's 15 league games this season.
Gomez, 21, will undergo a scan on his ankle on Thursday following a challenge from Burnley's Ben Mee in the first half, which Klopp said could keep the England worldwide out for a while.
Jurgen Klopp made seven changes to his side en route to victory over Burnley in midweek and is expected to use a number of fringe players once again with a crucial Champions League clash against Napoli and then a Premier League showdown with Manchester United to come next week.
Gomez was clattered by Robbie Brady before a strong Ben Mee challenge saw the full back hurtle into the advertising hoardings and leave on a stretcher midway through the first half.
"That's part of that front-foot mentality". Joe is injured and probably not only a little bit'.
Burnley manager Sean Dyche made no apologies for his side's approach as the hosts picked up just one yellow card, but Klopp added: "I'm pretty sure saying this won't make me a lot of friends here, but that's not the job I have".
"I said after the first challenge, I don't know who did it, a sliding tackle from six/seven yards, getting the ball, everybody likes it, I said to the ref "it's no foul but please tell them you can not do that".