The paper said police had confirmed that a 49-year-old man had been arrested on Monday on suspicion of possessing drugs but would not confirm his identity.
Rausing is the son of former Tetra Pak co-owner Hans Rausing, who helped shape the Tetra Laval group before selling his 50% stake in 1995.
The Financial Times reported today that Rausing was thought to have been questioned by police after his wife Eva was found dead in their Knightsbridge home.