According to Galloway, Khan had an affair with his aide Aisha Ali Khan and both were sleeping in his Streatham, South London house, while he was away in Indonesia.
Galloway claims the pair conspired to run a "dirty tricks" campaign against him and his Respect political party, the Daily Mail reported.
The MP has suspended Khan, 32, a mother of one, from her post, it said.
Besides making a formal complaint to the police, the MP has tabled a motion in Parliament calling on the Home Secretary to make a statement on the issue.
Scotland Yard said the officer has been placed on restricted duties pending an investigation by the Directorate of Professional Standards.