Greens senator Lidia Thorpe will refer herself to parliament's powerful privileges committee, over her undisclosed relationship with a former member of the Rebels outlaw motorcycle gang.

The ABC revealed last week that Senator Thorpe "briefly dated" a former president of the club's Victorian chapter, while also serving on a parliamentary law enforcement committee.

That committee was receiving confidential briefings and documents, however, there is no suggestion that Senator Thorpe passed information to anyone who should not have received it.

Within an hour of the ABC's report, Senator Thorpe had resigned as deputy leader of the Greens in the Senate.

Today, she told the Green's party room that she will refer herself to the privileges committee, and is happy for an inquiry to take place. 

In a statement, she said that she had "made mistakes" and had not "exercised good judgement".

"I have decided to write to the president of the Senate today requesting a referral of myself to the Senate Committee of Privileges," Ms Thorpe said in a statement. 

"The Greens Party Room backed my decision today.

"I am more than willing to participate in any inquiry."

Last week, the chair of the law enforcement committee, Labor senator Helen Polley, launched an internal investigation into any potential conflicts of interest.

That inquiry will include an examination of the minutes of previous meetings. 

The federal opposition has also flagged it will seek to move a censure motion when parliament returns tomorrow.

Censure motions allow MPs to express their disapproval of their colleagues but don't have any direct legal consequences.

It is not clear yet if the government will support the motion.

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