Irving missed 26 games earlier in the 2019-20 NBA season because of the injury.
The 27-year-old Duke product hasn't played for the Nets since a Feb. 1 loss to the Washington Wizards because of a separate knee injury, and Atkinson sidestepped a question about whether the guard could miss the remainder of the campaign.
"I don't want to go there," he told reporters.
A long-term absence would be a major setback for Brooklyn (25-28), which owns the seventh seed in the Eastern Conference. It holds a two-game edge over the Orlando Magic and a five-game advantage over the Wizards, the ninth seed.
Irving has enjoyed a terrific debut season with the Nets after he signed a four-year, $136.5 million contract in July. He's averaging 27.4 points, 6.4 assists, 5.2 rebounds and 1.4 steals per game while shooting 47.8 percent from the field across 20 appearances.
Spencer Dinwiddie, Caris LeVert and Jarrett Allen have also played well for Brooklyn, which has turned an expected transition year while Kevin Durant recovers from a torn Achilles into a potential playoff berth.
The Nets don't fall into the exclusive group of championship contenders even with a healthy Irving, though. It's going to take him, Durant and potentially one more marquee addition to reach that level, and that could be a factor if Brooklyn has to decide whether to try to get Irving back on the court this season.
As the team awaits word on his status, it also prepares to return from the All-Star break Thursday night with a road clash against the Philadelphia 76ers.