Potential buyers for the Newcastle-based large-format company, which went into administration on 5 January, have until the end of today to make a bid.
Ian Brown, administrator for Deloitte, told PrintWeek: "There are a couple of people in the frame and we are optimistic that we'll find a good buyer.
"We are expecting another two bids from interested trade buyers and we're not ruling out surprise bids.
"We can't say how long it will be before we decide on a deal – that depends on the shape of the offers."
NSL cut 22 jobs after losing key work from Woolworths and other major retailers.
Business is said to have been steady since the administration.
Brown last week revealed it had sent out 30 information memorandums and had "over a dozen" parties look round.
Deloitte is currently working with David Moorhead, NSL's production director, to run the business and find a buyer.
Duncan Hesse, NSL's managing director, no longer plays an active role in running the business.
NSL was founded by chairman Bill Hesse in 1972. In 1998 it moved into its current site. NSL runs a 6900sqm factory on the New York Industrial Estate, North Tyneside.
NSL offer tabled as deadline for buyers looms
Administrators for Norscreen, which trades as NSL Integrated Print Solutions, have received one offer and are expecting "a couple more", as the deadline for bids approaches.
