"Every good fighter knows when to hang up their gloves, and for me, that time is soon approaching", Hatch said in a video posted on Twitter.
"I didn't see Governor Romney file papers to run for Orrin Hatch's seat".
Romney maintains residence in Utah and was the president and CEO of the Salt Lake City Olympic Committee before going on to serve as governor of MA and challenge Barack Obama as the Republican nominee in the 2012 presidential election. He is also the second-longest serving senator in the USA history.
Romney wasn't tipping his hand on social media on Tuesday, preferring to praise Hatch for his long service.
Hatch chairs the powerful Senate Finance Committee and was a major force in getting a tax overhaul through Congress and signed into law in December.More news: Bears likely ousting John Fox at end of season, report says
At a rally for Alabama Senate candidate Roy Moore, Bannon called Romney, the GOP's 2012 presidential nominee, a draft dodger who "hid behind" his religion.
Romney's statement did not mention his own plans.
Bloomberg News reported in October that Bannon was planning to play in nearly every Republican Senate primary contest, anyway, but a couple of the Breitbart News chief's would-be targets - Sen.
In the statement announcing his decision to retire, Hatch cited work helping create the Americans with Disabilities Act, expanding children's health insurance and expanding use of generic drugs.
Last month, Hatch reveled in the spotlight as chairman of the Senate Finance Committee while shepherding a massive tax bill through the Senate - attention, friends and colleagues said, that made him lean toward running again.More news: Mega Millions, Powerball jackpots swell to $800M
White House Press Secretary Sarah Huckabee Sanders said Hatch's leadership will be greatly missed. "Ann and I wish Senator Orrin Hatch and his loving wife Elaine all the best in their future endeavors".
Other conservatives in the state have been trying to recruit another conservative challenger to contest Romney from the right, but no candidates have yet come forward.
As the president prodded Mr. Hatch to stay, voices in his home state were urging him to go.
Mr. Romney was unaware of Mr. Hatch's decision and of late had been operating under the assumption that the senator would run again, not even bringing up the possibility of a campaign while skiing Monday with friends in Utah. Hatch earned about $39,000 in royalties from his songs in 2005.More news: Raiders looking to reunite with Jon Gruden
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