Snow's job has seemingly been in limbo when it was included in possible administration changes during a cabinet shakeup earlier this year.
The Washington Post reports Snow had first told a top aide to President Bush in December he would stay on through January 2006 and wanted to put a stop to any rumors.
Snow has been in the job for three years, replacing Paul O'Neill, a man who sometimes differed from the White House line on items like tariffs and tax cuts.
Bush denied he knew of Snow's plans but applauded him Thursday for his work while the economy grows, although wages are dropping when adjusted for inflation.
A nominee to replace Snow could come from a list of current and former administration officials with ties to the private sector.