SuperValu say their stores may experience supply issues because of a price dispute with Unilever.
The supplier has already stopped deliveries to all UK Tesco stores after increasing their prices to deal with the falling value of the pound.
SuperValu say the price increase is not justified, and that a drop in price is actually needed given the current exchange rate.
They have warned customers they may experience supply issues as negotiations with Unilever continue.
The supermarket said: "Negotiations with Unilever are continuing and we are examining all options open to us.
"We would stress that this is not our desired outcome, but we do not believe a price increase on the products under discussion is justified given the current exchange rate.
"In fact, we believe that a price decrease is warranted given the fall in the value of sterling against the euro."
Tesco Ireland told Newstalk.com that it was "not appropriate to comment on commercial relationships with individual suppliers".
Unilever are also believed to have requested a price rise for its products from Dunnes Stores.
However, Dunnes rejected it brining into question the supply of Unilever's products in their outlets.
It comes as Unilever's finance chief , Graeme Pitkethly, said: "In the UK, which accounts for 5% of turnover, prices should start to increase to cover the cost of imported goods due to weaker sterling."
However, he added that he is confident that the dispute with Tesco in the UK will be "resolved very quickly" and said that other Unilever customers have accepted price hikes.
The group, behind brands such as Marmite, Flora and Persil, is believed to have demanded a 10% price rise due to the falling value of sterling, halting deliveries to Tesco when it refused.
Since the EU referendum on June 23, the pound has lost nearly 18% of its value against the dollar.
The stand-off has left the supermarket facing a shortage of brands such as Surf washing powder, Comfort fabric conditioner, Hellmann's mayonnaise, Pot Noodle and Ben & Jerry's Ice Cream.
Mr Pitkethly's comments came as Unilever reported a rise in sales in the third quarter, helped by price increases.
The firm said underlying sales rose 3.2% in the period, with total sales coming in at €13.4bn. However, the firm added that it took a hit from currency movements.
Earlier this year, the firm posted profits of around €2.2bn for the first half of 2016.
Chief executive Paul Polman warned in June that a vote to leave the EU's single market would increase prices for consumers in the UK.
He said that a vote to Leave would mean hikes in import duties on items such as dairy products, leading to price rises that would affect consumers there.