The top cops to face allegations include ADGP MR Ajith Kumar, Malappuram SP Sasidharan and Pathanamthitta SP S Sujith Das.
Vijayan has ordered a probe into Ajith Kumar.
As per reports, Kumar met the Chief Minister and asked for a probe into the allegations against him.
He has directed the formation of a high-level team to investigate the allegations.
The Chief Minister has asked for the completion of the probe and submission of a report within a month.
In a fresh allegation, Anvar sought the source of the money with which Ajith Kumar built an expensive mansion in a posh area of the capital city.
Anvar released several audio tapes of telephonic conversations claiming Ajith Kumar was embroiled in illegal activities.
The ruling CPI-M has said all allegations will be probed and an appropriate stand will be taken.