William Rehnquist (AP Photo)
The 80-year old chief justice is currently battling thyroid cancer.
The development Wednesday comes as President Bush continues to research choices to replace another judge on the nation's highest court, retiring Justice Sandra Day O'Connor.
President Bush said Wednesday he anticipates continued consultations with lawmakers and advisors before picking a candidate.
Both liberal and conservative lobbing groups have launched multi-million dollar campaigns to try to influence Mr. Bush's choice.
For his part, President Bush has said he will not pick a candidate based on his or her position on a specific issue, such as gay marriage or abortion. He has also urged the Senate to ignore the enormous pressure from special interest groups. The Senate must confirm any nominee.
Some information for this story provided by AP.