"We have not yet been in a position to interview Mr Rausing," said Detective Inspector Sharon Marman to Westminster Coroner's Court, according to The Telegraph newspaper.
"He has been arrested on suspicion of her murder and we await notification of when he would be fit to be interviewed by police."
An inconclusive post mortem has been carried out on the body of 48-year-old Eva Rausing, with further toxicology tests on the way.
Police have revealed suspicions that the woman lay dead in her bedroom for up to one week before she was found dead during a drug raid.
The raid was carried out by London police after Hans Kristian Rausing, 49-year-old heir to the Tetra Pak empire, was stopped puller over in his car after driving erratically.
His car was then searched, and drugs were discovered in the vehicle.
Rausing was moved from the police station to Maudsley Hospital in southern London on Tuesday for care.
The deceased woman was the daughter of a wealthy Pepsi Cola executive whose family live on an exclusive island off the South Carolina coast in the United States.
Rausing and his wife, who met in a US addiction clinic, spent much of their time in Barbados, where they owned an 11-bedroom mansion.
The family, headed by Rausing's father Hans, is worth 4.3 billion pounds ($6.64 billion), according to this year's Sunday Times Rich List.