Rehnquist, 80, hasn't decided whether to sit for arguments, court spokeswoman Kathy Arberg said Friday. She did not provide any update on his condition.
This is the first time in months the court hasn't unequivocally declared Rehnquist would not be on the bench when justices hear arguments.
Rehnquist last sat for cases in the fall. He was hospitalized Oct. 22 and underwent a tracheotomy to help him breath.
He has been working regularly at the court for many weeks, presiding over private meetings of the justices, reading transcripts of the arguments and voting on decisions, but not appearing for arguments.
Rehnquist, looking frail, made his first and only public appearance since the fall in January, when he swore in President Bush.
Earlier this week, Rehnquist presided over a two-hour, closed-door meeting of the Judicial Conference of the United States (search), the policy-making body of the federal judiciary. Attendees say he showed good humor and moved under his own strength.
Rehnquist's illness has led to speculation that he will step down, giving the court its first opening since 1994. While such an announcement could come at any time, justices typically wait until the term ends to leave to avoid an extended vacancy and the possibility of 4-4 votes.
The court will hear arguments in the next two weeks on whether file-sharing services should be held responsible when their customers illegally swap songs and movies online. It will also revisit the death penalty when justices consider how U.S. authorities should deal with foreign nationals facing charges that could result in execution.