With a few personnel shifts going on in the White House, there's speculation that presidential spokesman Scott McClellan may be looking to step down.

One of the people the White House has approached as a possible replacement for McClellan is FOX News Radio host Tony Snow. The White House discussed the possibility with Snow as recently as this week.

Snow, who hosts "The Tony Snow Show," once served as a speechwriter for President George H.W. Bush.

Other people have also been approached about the position, including former Pentagon spokeswoman Victoria Clark and Dan Senor, the former Coalition Provisional Authority spokesman in Iraq, who served the U.S. civil administrator in Iraq, Paul Bremer.

McClellan, who has been press secretary for two years, refuses to speculate about his own future. But he has acknowledged that he has held the job for "a long time."

A spokesman switch would come as new White House Chief of Staff Josh Bolten is looking to solidify a staff by meeting with all personnel members individually about their futures in the Bush administration.

Bolten, who took over for Andy Card as White House chief of staff late Friday, told staffers on Monday that if they thought they would leave their posts in the near future, they should do so soon.

On Tuesday, President Bush tapped U.S. Trade Representative Rob Portman for the head of the Office of Management and Budget. Susan C. Schwab, a deputy USTR, has been chosen to take over for Portman. Also, Jim Towey, head of the White House office of faith-based and community initiatives, resigned to become president of St. Vincent College in Pennsylvania. Several former high-ranking U.S. military generals have in recent weeks called for Defense Secretary Donald Rumsfeld's resignation, but Bush has stepped in and said he has the utmost confidence in his Pentagon chief.

FOX News' Carl Cameron contributed to this report.