The former president said on Sunday that he would speak from Florida on Tuesday following his appearance in New York.
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Mr Hutchinson used an interview which also aired on Sunday to announce his bid to rival Mr Trump in the race to be the Republican candidate in the 2024 US presidential election.
He told ABC’s This Week: “I’m running because I believe that I am the right time for America, the right candidate for our country and its future.”
The 72-year-old, who left office in January after eight years as governor, said he would make a formal announcement in April in Arkansas.
He has ramped up his criticism of the former president in recent months, calling another Trump presidential nomination the “worst scenario” for Republicans and saying it would likely benefit President Joe Biden’s chances in 2024.
Mr Hutchinson’s home state is still reeling from recent devastating tornadoes, with the death toll continuing to rise across US states hit by the extreme weather.
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In addition to Mr Trump, Mr Hutchinson joins a Republican field of confirmed candidates that so far also includes former UN Ambassador Nikki Haley and entrepreneur Vivek Ramaswamy.
Controversial Florida Governor Ron DeSantis is also expected to jump into the race in the summer, while US Senator Tim Scott of South Carolina and former Secretary of State Mike Pompeo are among those considering bids.
As governor in Arkansas, Mr Hutchinson championed a series of income tax cuts as the state’s budget surpluses grew.
He signed several abortion restrictions into law, including a ban on the procedure that took effect when the US Supreme Court struck down Roe v Wade last year.
Mr Hutchinson has said he regretted that the measure did not include exceptions for rape or incest.
Although he has supported Mr Trump’s policies, Mr Hutchinson has become increasingly critical of the former president’s rhetoric and lies about the 2020 presidential election.
He said Mr Trump’s call to terminate parts of the Constitution to overturn the election hurt the country.