Quickly responding, a Perry spokesman called the senator "Kay Bailout" - a reference to her vote for the $700 billion Wall Street rescue - and said she "has been talking about running for governor and passing legislation for years and neither has ever happened."
"Today she continues her streak of indecision," Mark Miner said.
Hutchison is establishing a committee to explore a possible run and is transferring $1 million into it from her federal campaign account, which had about $8.7 million at the end of September.
"Texas has not really had a scrubbing of our state government, really in years and years and years," Hutchison told Dallas television station KXAS on Thursday. "I think we need to prioritize spending. Right now the priorities should be education and transportation and access to health care."
Perry reported almost $3 million on hand at the end of June. He is not required to file an update until January; a spokesman declined to release the current total.
Hutchison told Dallas television station WFAA, "I have seen the races that Gov. Perry has run before and I would not like that kind of race. But am I tough enough to do it? Absolutely."
Perry was lieutenant governor when Bush resigned after his election to the White House in 2000.
Hutchison joined the Senate in 1993 in a special election to succeed Democrat Lloyd Bentsen, who became treasury secretary in the Clinton administration. The first and so far only woman elected to represent Texas in the Senate, she won her first full six-year term in 1994 and re-election in 2000 and 2006, with more than 60 percent of the vote each time.
Considered one of the state's most popular politicians, she has run into opposition among Republicans for her support of abortion rights. Previously she was the Texas state treasurer.
Hutchison has said she may leave the Senate as early as next year to campaign. Her term ends in 2012. If that happens, Perry would appoint a replacement to the seat until an election is held.