Supermarket giant Asda is considering entering the Republic of Ireland by offering a home delivery service.

The retailer told specialist publication Retail Week that "offering home shopping to Irish customers is something we would love to be able to do. It isn't something we anticipate we will be able to resolve in the short term but our fingers are crossed that we can offer the benefits of our great value offer through home shopping as soon as we possibly can".

Asda, which is owned by Wal-Mart, will have to adapt its online model to accept payment in euro before the service could be introduced. Its entertainment division already offers free delivery to addresses in the Republic of Ireland.

Asda has been one of the main beneficiaries of the surge in the number of cross-border shoppers seeking to take advantage of the weakness in sterling. Asda and Sainsbury's already account for 2.5% of the Republic's grocery market, according to figures from TNS Worldpanel, even though neither has a single shop here.

Asda's Enniskillen shop is the sixth-best performing shop in the entire Wal-Mart portfolio and Asda chief executive Andy Bond has said that some of its shops in Northern Ireland generated 50% of their sales in euro.

The Sunday Tribune revealed last November that the retailer had begun looking for a site in Newry to open a new supermarket and take even more advantage of the shoppers coming from the south. At the moment, most shoppers from Dublin tend to travel to Sainsbury's in Newry whereas shoppers in Connacht, Donegal, Cavan and Monaghan tend to travel to the Asda shop in Enniskillen.

There has been sustained speculation about a bid for Dunnes Stores by Asda but both companies have refused to comment. Dunnes has been gaining market share in the grocery trade as it drives prices down but industry sources say the drapery and homewares sides of the business are struggling.

The retailer has been closing older and underperforming shop, including its homewares store at South Great Georges Street in Dublin, where its signage has been covered over, and its Grafton Street shop, as well as older shops in Dundalk, Wexford and two branches in Limerick.

Wal-Mart told investors last week that Asda's comparable sales growth was 6.5% last year and that it has outperformed the general market since then via a combination of more visitors to the shops and a higher average shopping bill. On the clothing side, its George brand, which has featured Wayne Rooney's wife Coleen McLoughlin, has also managed to increase market share.