BED went into administration with Colin Wilson of Tenon Recovery on 9 July 2009.
A number of companies are believed to have initially shown interest, but that list has been whittled down to two, according to Wilson.
He said: "We are trying to finalise an offer with one party, but we are also looking at another offer as well. Hopefully we will agree terms of a contract by [today] or Tuesday."
Wilson confirmed that the offer that was closest to be accepted was that of Crossways Envelopes, a company set up by BED directors Nigel Harper and Gary Butters. Wilson said that Crossways was "getting its ducks in order".
He would not be drawn on the other offer, which is understood to have been below expectations, but he did confirm that it was from within the print industry.
Wilson added that BED, which has been operated under license by Crossways, has been "going well".
He said: "They were quite weak when they started, while they were getting everything in order. But they are doing well at the minute."
Meanwhile Bespoke Envelopes, a connected company which is understood to have employed around four staff, is set to go into liquidation on 25 August.