Of the 300 staff at the firm, 130 have been made redundant.
"There was very little interest in that side of the business and several publishers, including Cond Nast, have now gone elsewhere," said administrative receiver Richard Neville of Neville Hatton & Co.
A deal could be tied up next week for the rest of the business, which is automated and includes shrink wrapping. The firm would not reveal the identity of the possible buyer.
Rumours that St Ives was in the frame to buy Ailec have been dismissed by the group as "just speculation".
Ailec Mailing Services went into administrative receivership a fortnight ago. The move was due to cost escalations because of the minimum wage, business rates and energy costs.
Story by Philip Chadwick
Ailec lays off staff but buyer is on the cards
The administrative receiver for Ailec Mailing Services has closed the hand finishing side of the business but is in very serious negotiations for the remainder of the business.
