The investigation spans separate incidents alleged to have taken place between the 1980s and 2015 both in London as well as outside of the UK.
The Hollywood film producer has “unequivocally denied” all allegations of non-consensual sex.
No arrests have been made over any of the allegations at this stage so far, the Metropolitan Police said.
The names of the complainants or alleged offences at this stage are currently kept secret.
Numerous allegations have been made against the movie mogul by women including actresses Angelina Jolie, Rose McGowan and Gwyneth Paltrow.
On Tuesday, the Producers Guild of America said Weinstein had been banned for life over reports of his “decades of reprehensible conduct”.
Actress Rose McGowan says she was offered $1m (£760,000) from Harvey Weinstein in exchange for her silence.
McGowan says she turned down the money the day before the New York Times ran an expose on the movie mogul earlier this month.