Seven bids have been received for the UK arm of the business, with Tata operating a number of plants including one in Stocksbridge and two in Rotherham.
Prime Minister David Cameron said: "There has been an encouraging number of serious offers coming through.
"We have just got to stick at it and do everything we can to try to bring this to a successful conclusion.
"As I have always said, there are no guarantees, we can't guarantee this is going to work but we are doing everything we can."
Business Secretary Sajid Javid has travelled to Mumbai to meet Tata officials today.
The firm is expected to make a shortlist of bidders today.
Selling Tata's UK assets would secure 11,000 jobs.