On Friday, the scandal surrounding Weinstein - who produced films including Pulp Fiction, Shakespeare in Love and Crouching Tiger, Hidden Dragon - deepened when he was accused of rape by US actress Rose McGowan.
He was already facing claims of rape, sexual assault, groping and harassment.
Weinstein, who is believed to be in Europe seeking therapy, has insisted through a spokeswoman that any sexual contacts he had were consensual.
Since the avalanche of claims began, the company has been trying to disassociate itself from its co-founder and save the business, reports say, with efforts made to buy Harvey Weinstein out, rebrand and keep creative partners on board.
But reports in the Los Angeles Times said that financers had begun to pressure the company to sell and potential buyers were circling.
The Wall Street Journal also reported the company was "exploring a sale or shutdown" and was "unlikely to continue as an independent entity".
The company is thought to be worth hundreds of millions of dollars but before the recent allegations had already faced questions about its future prospects amid increasing competition from media streaming services.
Investment bank Goldman Sachs said on Friday it was investigating options to sell the small stake it holds, citing the reported "inexcusable behaviour".
On Saturday, the organisers of the Oscars film awards will hold emergency talksamid speculation it could suspending Harvey Weinstein's membership. Bafta, the British Academy of Film and Television Arts, has already done so.