Senate investigators are pondering how to proceed with Rohrabacher, in part because the California Republican is a member of Congress, the sources said.
Rohrabacher met with Assange earlier this month in the Ecuadorian embassy in London, where Assange was granted asylum after Sweden sought to question him in a rape investigation that has since been dropped.
Assange said, according to Rohrabacher, that he was not behind the leak of Democratic National Committee emails last year.
Shortly after the meeting with Assange, Rohrabacher said he planned to debrief President Donald Trump on their talk. Speaking on Sean Hannity's radio show this week, Rohrabacher said that other parties are planning a "rendezvous" for him and Trump to speak about the Assange meeting.
There is no indication that Rohrabacher is being investigated by Special Counsel Robert Mueller. But Rohrabacher does have connection to a person involved in something that has drawn the interest of investigators: the June 2016 meeting that Donald Trump Jr., Trump son-in-law Jared Kushner and then-Trump campaign chair Paul Manafort had with a group of Russians, including lawyer Natalia Veselnitskaya.
Rohrabacher was not at that Trump Tower meeting, but he was working closely to try and repeal the Magnitsky Act, which targets Russians whom the US considers human rights abusers -- the same thing Veselnitskaya was actively lobbying to undo.
After publication of this story, Ken Grubbs, a spokesman for Rohrabacher, insisted the congressman was not working closely with Veselnitskaya.
Grubbs told CNN earlier Wednesday that Rohrabacher would be happy to talk with the Senate Intelligence Committee.
"He hasn't been contacted by the committee, but is happy to talk with them after he talks with President Trump," Grubbs said.
Update: This story has been updated to reflect that Grubbs disputes that Rohrabacher was working closely with Veselnitskaya.