The memos written by a former British intelligence agent and Russia expert, Christopher Steele, made a series of allegations, including multiple secret meetings between Trump campaign officials and Russian agents.
Graham, Grassley and some other Republicans have used official resources to investigate the Steele dossier, Trump critics and officials working for the Federal Bureau of Investigation and Mueller.
The senators' referral states: "Based on the information contained therein, we are respectfully referring Mr Steele to you for investigation of potential violations. for statements the Committee has reason to believe Mr Steele made regarding his distribution of information contained".
In a cover letter to Deputy Attorney General Rod Rosenstein and FBI Director Christopher Wray released by the committee, the senators say the referral relates to "certain communications between Christopher Steele and multiple US news outlets regarding the so-called 'Trump dossier.'" The rest of the referral is classified and was not released.
Instead of focusing on the Russian Federation claims, Simpson said, key Republicans have instead made him the focus of their investigations.
"Everyone needs to follow the law and be truthful in their interactions with the FBI", Grassley said in the letter.
The dossier, which began as an opposition research effort and became publicly known in early 2017, details Russian interference in the 2016 election and includes allegations that Russian operatives claim to have compromising personal and financial information about Trump.
The minority leader of the Judiciary Committee, Sen.
The dossier was turned over to the FBI in 2016, and federal investigators worked to corroborate portions of it.
There are now three ongoing congressional investigations into allegations of Russian interference in the election and complicity by Donald Trump's campaign team. "The rule of Law depends on the government and all who work on its behalf playing by the rules themselves".
Republicans allege the dossier, which was commissioned by research firm Fusion GPS, served as the basis of the federal investigation in the president's alleged ties to Russian Federation. Nunes' committee has been seeking information about Steele's research for months.
In the letter released by the senators, Grassley and Graham neither identify anyone to whom they believed Steele lied nor do they identify any news outlet.
Simpson has testified before three congressional committees - albeit behind closed doors - and has explained how his clients, the Washington Free Beacon and the Clinton campaign, came to hire Fusion GPS, setting off the private investigation into the Trump campaign.
A criminal referral is a request to DOJ for further investigation, and is not alleging that a crime occurred.
Donald Trump has threatened to sue a publisher over a book he doesn't like.
Simpson added: "We're extremely proud of our work to highlight Mr Trump's Russian Federation ties".