Outokumpu, the world's second-largest stainless steel producer is planning to move new orders from Coil Products in the city to Finland, hitting UK jobs.
The move is temporary while UK shift patterns are reviewed, possibly allowing work to return to Sheffield.
Steel workers' union Community said they were currently entering talks with the firm.
Eero Mustala, the senior vice-president of Outokumpu said: "This is a temporary measure. There will be a review of shift levels.
"Eventually, this will mean job losses, but we're in negotiations with the unions at the moment."
Mr Mustala said he did not know how many jobs would go.
He added that there had been no redundancies so far.
The review comes against a background of fluctuating global demand for steel which has been driven by China for the past three years.
But the market there has seen a dip in the last few months.
Mr Mustala added: "We're going to review the situation by the end of the year and see how demand is continuing."
The firm will continue to produce some toughened grades of steel in the city.