The Newcastle-based large-format company went into administration on 5 January but has continued trading since then.
Administrator Ian Brown of Deloitte has said the business will close if a deal is not completed by the end of today.
He told PrintWeek: "We are currently still trading and are in talks with an interested party. We will know by the end of play today whether the party in question will make a bid for the business.
"We've been trading from administration for five or six weeks now. The staff have been fantastic, but we've reached a critical point where we can't continue to trade without a buyer."
The company went into administration on 5 January after losing contracts from retail clients including Woolworths. It cut 22 jobs as a result and now has around 50 staff, according to Brown.
Norscreen has an annual turnover of £10m, according to the PrintWeek Top 500 2008. It was founded by chairman Bill Hesse in 1972 and moved into its New York Industrial Estate, North Tyneside, site in 1998.
Make or break day for NSL as deadline looms
The administrator for failed printer Norscreen, which trades as NSL Integrated Print Solutions, has issued a final deadline to an unnamed buyer.
