Senator Thorpe didn't disclose a relationship with Dean Martin, the ex-president of the Rebels outlaw motorcycle gang, while she was sitting on a parliamentary law enforcement committee.
She will write to the Senate president on Monday saying she's happy for a privileges committee inquiry to take place.
The privileges committee investigates whether parliamentarians have complied with disclosure requirements.
The Greens partyroom supported her decision to take the action.
Opposition Senate leader Simon Birmingham had said he would attempt to refer her to the privileges committee.
There is also a review into whether Senator Thorpe received any confidential briefings about bikie gangs while sitting on the law enforcement committee.
Greens leader Adam Bandt sought and received Senator Thorpe's resignation as deputy Senate leader after the relationship was revealed.
One Nation senator Pauline Hanson is preparing to move a censure motion against Senator Thorpe this week.
Senator Hanson is also set to move an attendance motion requiring Senator Thorpe to attend the chamber and give an explanation about the nature of her relationship and why she kept it hidden.
The motion will call on Senator Thorpe to reveal whether she passed on any information received in briefings about outlaw motorcycle gangs or Mr Dean's associates while in the relationship.
Senator Thorpe can choose to address the Senate on her own volition ahead of the motion.
Finance Minister Katy Gallagher said the government was considering the motions and would come to its decision by Tuesday.
"This is a serious matter for the Senate, it's not something that can be dismissed lightly," she told reporters on Monday.
"We will be considering options about how to deal with the matter. We want to do it calmly, sensibly and rationally."
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