Essex police are investigating claims that the energy secretary had asked his then wife Vicky Pryce to take speeding penalty points on his behalf.
The Sunday Times had said that it would seek a judicial review of a crown court ruling last October ordering it to hand over evidence pertaining to the case.
However, it has now said that it will comply with the police production order in the near future.
Police delivered initial evidence to the Crown Prosecution Service last July, relating to a 2003 incident in which Huhne, then an MEP, is alleged to have asked Pryce to accept the three-point penalty.
The CPS has not yet made a decision on whether the Liberal Democrat MP should be charged for the alleged offence.
But director of Public Prosecutions Keir Starmer said in November that the body was waiting for the Sunday Times court case to be resolved.
Huhne has said that the allegations against him are "simply incorrect", but that he welcomes the police investigation as it will "draw a line under the matter".
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