Franks represents the 8th district of Arizona, which includes the northwest Valley.
It was not immediately clear why Franks was resigning.
The lawmaker has not yet confirmed or denied the resignation rumors, but Franks is expected to make a statement later on Thursday.
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Trent Franks, the dean of Arizona's House Republicans, is reportedly stepping down amid claims of inappropriate behavior.
"If this turns out to be true, there won't be that many people who are surprised", the Arizona Republican said, according to the report.
"There's been rumors swirling around him for years, at least in 2012", a Republican said.
Franks told Roll Call that a statement would be forthcoming.
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"Half of all black children are aborted", Franks infamously said in 2010.
Franks was first elected to Congress in 2002 and was reelected in 2016 by a 37-point margin.
Franks was spotted on the House floor during votes Thursday night, speaking with fellow Arizona Republicans Andy Biggs and David Schweikert. According to Census.gov data, the district is located in the northwestern part of Phoenix.
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Perhaps cushioning the blow somewhat for the Red Sox is that the Yankees have also been told they are out of the running. Ohtani is limited to a minor league contract because of restrictions imposed by the MLB collective bargaining agreement.