Following its move into administration last month, Chapman has said that discussions with a potential purchase continue and there are still several parties in play.
He said: "However, clearly something needs to happen soon as our summer ends this week and customers need deliveries to start again."
Curtis went into administration at the end of July and Blair Nimmo and Gary Fraser of KPMG Restructuring were appointed as joint administrators of the 135-year-old Guardbridge, St Andrews-based paper mill.
The £35m-turnover company had experienced significant losses in recent years and has been hit by the strong euro and the rising cost of raw materials.
Last month, the Scottish Government said it was willing to support any development to continue the operation at Curtis Fine Papers.
John Swinney, the cabinet secretary for finance and sustainable growth, made clear to the administrator the Scottish government’s willingness to support any development to continue the operation at Curtis.
Swinney also said that, as well as searching for a way forward to continue business activity, support is being made available to staff issued with redundancy notes.
Former Curtis MD says buyer for the mill must be found soon
Former managing director of Curtis Fine Papers Keith Chapman has warned that a purchase of the mill needs to happen soon if the company is to survive.