Franks told Roll Call that a statement would be forthcoming.
Franks' statement is expected to come Thursday night.
The statement is supposed to be released sometime on Thursday. Roll Call first reported that Franks was expected to resign.
One Arizona Republican reportedly said not many people would be "surprised" if he resigned.
"There's been rumors swirling around him for years, at least in 2012", a Republican official told the outlet.
Two Republican consultants also confirmed the decision to The Associated Press but both said they did not know why he was leaving.
Adult Film Star August Ames Found Dead At Age 23
She had earlier used social media to warn fellow female porn stars about working with men who have been in gay adult movies. Ames was born Mercedes Grabowski in Nova Scotia and worked in a bar before she joined the adult film industry in 2013.
The congressman serves on the Armed Services Committee and the Judiciary Committee, in addition to be a member of the House Freedom Caucus.
Rep. Trent Franks (R-Ariz) (left) during a hearing on the District of Columbia Pain-Capable Unborn Child Protection Act at Rayburn House Office Building in Washington on May 23, 2013.
Trent is now serving his eight term in Congress - he was first elected in 2002.
The deep-red 8th District, northwest of Phoenix, supported President Donald Trump by 21 points in 2016, according to calculations by Daily Kos Elections.
The governor is required to establish the date of the primary election within 72 hours of the seat being officially vacated.