Gobert was checked on Saturday by the Jazz medical staff and is showing progress to make a return.
He suffered the injury during a 107-95 victory over the Boston Celtics on Dec. 15, going to the floor awkwardly after appearing to get rolled into by teammate Derrick Favors early in the first quarter. As he tried to get back to his feet, Gobert fell back to the floor and rolled to his back before clutching his left knee.
Gobert had been expected to miss three to four weeks.
Gobert missed 11 games earlier this season with a bone bruise in his right knee.
The 2017 All-NBA second-team center is averaging 11.6 points, 9.6 rebounds and 2.3 blocks per game in his fifth NBA season.
ESPN's Adrian Wojnarowski and Chris Forsberg contributed to this report.