The police are to conduct interviews with "key individuals" over allegations that Chris Huhne tried to illegally evade speeding fines.
The Lib Dem energy and climate change has said it is "simply incorrect" that he encouraged someone else to accept penalty points in 2003 on his behalf to avoid a driving ban.
But detective superintendent Tim Wills said today: "There are many lines of inquiry to be taken and the team are still working to establish if an offence has been committed.
"Obviously this will entail speaking to key individuals identified by the inquiry team. It would not be appropriate to release any more information prior to progressing these lines of inquiry."
The inquiries follow a formal complaint from Labour MP Simon Danczuk.
It has been alleged that it was Huhne's wife at the time, Vicky Pryce, accepted the points on her licence.
The Lib Dem minister separated from Pryce last year after beginning a relationship with another woman.
On Monday Huhne said he welcomed the referral of the case to the police as he hoped it would "draw a line under the matter".
"I don't want to say any more than that, I think the police can get to the bottom of this," the energy secretary said.
Yesterday in the Commons Huhne's Labour shadow Meg Hillier littered a speech on energy with references to his troubles including accusing him of taking a "go-slow" approach.
And in a unfortuate piece of parliametnary timetabling for Huhne his appearence in the Commons chamber was followed by a discussion of the Dangerous Driving (Maximum Sentence) Bill.
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