The Reds defender also thanked fans for their support after he was forced off on a stretcher in Wednesday’s 3-1 victory over Sean Dyche’s Clarets.
Gomez went down under a hefty challenge from Ben Mee after only 23 minutes at Turf Moor.
It was feared that the injury might be extremely serious but he appears to have escaped the worst after it was revealed he will face only six weeks on the sidelines.
And the 21-year-old defender looked to be in a positive mood in a video posted on the club’s official Twitter account.
“I just wanted to say thank you to you all for your kind wishes and well-wishes,” he said.
“Obviously I’m gutted to have picked up the injury, but thankfully it’s not too serious and one that I can definitely be back stronger from soon.
“I’ll do my best to come back as quick as possible and hopefully be back with you guys soon, so thank you.”
Gomez has been excellent this season and is now a regular in Jurgen Klopp’s Reds side and for England under Gareth Southgate.
He has played in all but two of Liverpool’s Premier League games this season as they made their best-ever start to a top-flight campaign.
And Reds boss Klopp admits his absence will be a huge blow.
“It’s just a shame for the boy,” the German said.
“He’s been in outstanding shape. He has helped us a lot. It could have been worse.
“Six weeks is massive for us, but it means he will be back for a big part of the season and that’s good.”
Gomez’s fellow centre-back Dejan Lovren will miss Saturday’s trip to Bournemouth, while Sadio Mane remains a doubt for the clash after missing the Burnley game.
Alex Oxlade-Chamberlain remains a long-term casualty and Klopp will also be without Rhian Brewster, Nathaniel Clyne and Dominic Solanke.
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