The 4.5 acre freehold site is on the Upton Industrial Estate in Poole. It comprises three industrial units with a total area of nearly 10,700sqm.
The sale by auction was reported in Dorset Biz News.
The auction is being handled by commercial property specialist Acuitus, which has put a £3.25m estimate on the lot.
The units became vacant earlier this year after Walstead Group closed down the web offset printer in response to the reduction in magazine printing volumes.
Walstead made the decision to close the site before the Covid-19 pandemic struck.
The auction will be live-streamed on 23 September.
Walstead acquired Southernprint from Newsquest in the summer of 2009. At the time the site was owned by Newsquest. It is now owned by a property company.