The redundancies would come into effect next year.
Areas of work affected by any changes include petrol, bakery, back office and so-called hosting.
Jobs in the George areas of Asda stores could also be affected, it is understood.
The company declined to comment on any potential job cuts.
A statement said: "In a competitive retail market, where customers rightly expect great value and ease of service, we must always look at how we can work more quickly and efficiently for them - and, inevitably, that means we need to consider changing the roles we need our colleagues to do or the hours needed in particular parts of our stores.
"We believe the proposed changes we are consulting on would allow us to do a better job for our customers.
"We also recognise that discussions about potential change aren't easy. If the decision is taken to implement the proposed changes, we would work with our colleagues to look at the potential impact of these proposals on them."
In September 2017, cuts saw 300 staff based at head office Asda House in Leeds city centre lose their jobs and leave with 'boxes in hand'.
It's the second major blow to hit the company this month after it was announced that the proposed route of the HS2 railway line would potentially require the demolition of the firm's headquarters and the nearby Hilton Hotel.
Asda and rival Sainsbury's announced plans for a merger earlier this year - but assured staff that no job losses would result from the move.
They were also forced to deny rumours that Asda House would close and the head office be relocated elsewhere if the merger went through.