Brown Thomas is part of the Selfridges Group
However, it is not clear if the proposed purchase would include the entire group or just the UK and Irish assets.
The surprise approach was unsolicited, the Financial Times reported, and Credit Suisse has been appointed an advisor.
Brown Thomas was bought by Galen and Hilary Weston in 1971, with Arnotts joining the Selfridges Group in 2015.
Galen Weston passed away in April of this year, aged 80.
His daughter Alannah is chairman of Selfridges Group.
In the year to the February of last year, Brown Thomas Arnotts Ltd made a profit of almost €5m.