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Although no deal has yet been signed, the retailer — which was taken private earlier this year — is in advanced negotiations to buy the site.
INM wrote to potential buyers last month inviting them to bid for the landmark site.
Arnotts, which already operates the third-largest store in Ireland and Britain and is situated next door to the INM building, was always the most likely company to complete the purchase.
A deal could raise more than €20m for INM, which is struggling with an onerous debt burden. The media company’s net debt reached €1.3 billion last year after a spending spree.
A number of issues are complicating the sale. The first concerns the fate of the 320 staff currently working in the Middle Abbey Street offices.
These are mainly editorial staff working on the Irish Independent, Evening Herald and Sunday Independent titles.
Although no new home has been found for these staff, INM management is said to favour city-centre premises such as the nearby Irish Life Centre.
The company is also believed to be looking outside the city centre at sites in the docklands.
The second issue for INM is environmental. The firm has begun dismantling the Middle Abbey Street printing presses. It is understood, however, that the print residue may mean the new buyer has to take on the building without any environmental warranty.
The third issue for Arnotts concerns the listed facade. This will make it much more expensive to redevelop the building. Sources said the internal part of the building would have to be gutted if it is to be used as a retail space.
Arnotts is working with a property developer to reduce the cost of redeveloping the building. Liam Carroll of Zoe Developments was seen in the building last week.
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