The Indian steel giant has been suffering from plant closures across the UK in the face of a crisis gripping the British steel industry, largely due to cheap Chinese imports.
On Friday, Welsh's national assembly member Bethan Jenkins on her Facebook page said: "Am hearing that there is to be an announcement of job losses at Tata on Monday. The number I have been quoted is 750 jobs.
The Port Talbot unit, which employs around 4,000 workers, is the latest to be hit and a survival plan is expected to be worked out next week.
The company however said it had "no announcement to make at present".
"We don't have an announcement to make and when we do make one we will make it directly to the people affected," BBC quoted a spokesperson for Tata Steel in Wales as saying.
Welsh economy minister Edwina Hart said: "If we have an announcement from the company, the government will respond appropriately. Steel has been in crisis for a long time - this is not just a new thing."
Thousands of jobs were lost last year with cutbacks and the closure of steelworks in England and Scotland involving Tata and other UK-based steel companies. Steel unions have called for urgent action from the UK government to prevent further job losses.
Rob Edwards, lead organiser of the Community trade union, said: "The problem is there's cheap steel imports from China, all the business rates are wrong, the environmental taxes are wrong.
Tata Steel Europe employs 17,000 in the UK, with 6,360 of those across its plants in Wales. In October last year, the firm had announced that it would cut nearly 1,200 jobs at its plants in Scunthorpe in northern England and at Lanarkshire in Scotland.
Tata Steel is in talks to clinch a deal for the sale of some of these units.
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