Stefanik, whose representative did not respond to a request for comment, could announce the bid in a video as early as Friday, and has informed allies of her plans to seek New York's highest office.
Stefanik has relentlessly attacked Hochul in the run up to her long-awaited announcement, which she said would not come until after this week's election.
She could face a spirited primary from Nassau County Executive Bruce Blakeman, who said Wednesday he was also considering a run after winning reelection.
The announcement comes days after Zohran Mamdani was elected mayor, and is expected to be a target of Stefanik as she attempts to tie him to Hochul.
Stefanik, who was briefly nominated for a position as UN ambassador by President Trump earlier this year, has called Mamdani a "communist," among other attacks, and blasted Democrats "radical" agenda in Albany.
The upstate New York congresswoman, a one-time staffer for Mitt Romney's 2012 presidential campaign who helped Paul Ryan prepare for his vice-presidential debate, gained prominence in the MAGA movement during the first Trump administration, as a vocal defender of the president on the House Intelligence Committee during Democrats' first impeachment inquiry in 2019.
New York last elected a Republican governor in 2002, when George Pataki won a third term in office.
ABC News contributed to this report.
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