The pub, which is beside Bunratty Castle on the Limerick-Shannon road, is owned by Limerick businessman Humphrey O’Connor.
He bought it more than 25 years ago for IR£1million, then a record price for a pub. It is believed the asking price this time round is in excess of €12m.
Two Co Clare businessmen are understood to be among the frontrunners trying to purchase the pub in a private sale.
Film stars, political leaders and sports celebrities from all over the world have over the years been attracted by the old-world charm of the pub, which dates back to 1620.
The eponymous widow is said to have invented poteen, which she distilled in a wooded area nearby. In those days, the pub was an unlicensed shebeen.
The building was erected as a toll house and travellers using the bridge over the Owengarney river had to pay a toll.
Businessman Roger Porritt owned it for a number of years and built up its reputation for excellent food.
It became famous for its nightly sing-songs, which were a huge attraction for foreign visitors.