Arnotts and Brown Thomas could end up with new owners, as reports from the UK suggest that the Selfridges Group could be sold.
The price tag for the group - which owns the two well-known Irish department stores, along with the Selfridges stores in the UK - is expected to be in excess of £4 billion sterling.
The group is currently owned by the Canadian billionaire family the Westons.
Newstalk's Deputy Business Editor Gavin McLoughlin told The Hard Shoulder reports are suggesting the Weston family is being advised by Credit Suisse after an "unsolicited takeover approach" by an unnamed potential buyer.
He said: "This story is coming out of the specialist property publication React News... with The Telegraph and others picking up on it.
"The Telegraph says Brown Thomas and Arnotts are included as part of what's potentially up for sale here.
"Then you get into the fun of who is going to be involved here. The Daily Telegraph quotes a senior property source who says it might be Amazon who comes in to buy this thing... they've been taking steps into physical retail.
"Could it be a luxury goods company like Louis Vuitton Malletier... or could it be a Chinese or Middle Eastern buyer?"
Gavin said such stories can make for a nervous time for staff.
However, he noted that the Arnotts and Brown Thomas brands are quite strong, and higher-end retail appears to be faring well at the moment compared to some other retailers.
The Weston family's business empire spans Europe, the Americas, Australia, China and southern Africa, with the Irish members consistently named as Ireland's richest family.