Mueller is directing the Department of Justice's Russia probe and Franks claimed he is violating a law prohibiting him from serving if he has a "conflict of interest," according to the website.
Franks, a member of the House Judiciary Committee, maintained the law bars "a personal relationship with any person substantially involved in the conduct that is the subject of the investigation or prosecution," The Hill said.
A May 18 story by Fox News said Mueller and ousted FBI Director James Comey have had a long and close relationship dating back to 2003.
And The Hill noted Mueller's investigation has expanded to include President Donald Trump's decision to fire Comey.
"Bob Mueller is in clear violation of federal code and must resign to maintain the integrity of the ...