Dewhurst was talking to reporters Thursday when he was handed a note saying Hutchinson, a Republican, decided not to seek reelection, The Dallas Morning News reported.
Asked then about his political plans, Dewhurst said he is focused on the state's 140-day legislative session, which began Tuesday.
"I'm really focused right now on the session," Dewhurst said. "I've got my plate full."
However, a few hours later Dewhurst issued a statement clarifying his comments to reporters at the news conference.
"I fully intend to explore running for the United States Senate," Dewhurst said. "And should I run, I will run with the intention of winning."
Another Republican candidate is Roger Williams. In an interview Thursday, he expressed confidence he can raise the several million dollars needed to campaign for Hutchison's Senate seat.
"I take nothing for granted," he said. "It's going to be hard, whether there was an incumbent in the race or not, it was not going to be easy."
Hutchison is the first incumbent up for re-election in 2012 to retire, The Washington Post reported.
"I am announcing today that I will not be a candidate for re-election in 2012," Hutchison said in a statement Thursday. "That should give the people of Texas ample time to consider who my successor will be."
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