Labour mediator Juhani Salonius said his compromise proposal covered all the main sticking points in the dispute, such as operating plants through all public holidays and outsourcing work.
The aim is to clinch a three-year labour contract.
Salonius said that drawing up a compromise proposal had been extremely difficult.
If both the Finnish Forest Industries Federation and the Paperworkers Union accept the proposal, paper and pulp mills will start operating on Monday morning.
Exception to Lockout Limited production was resumed on Wednesday. The two sides agreed to re-start manufacturing cardboard to alleviate a shortage of packing material in the food industry. About 10 plants will churn out cardboard boxes. Sympathy Strike Action
Meanwhile, the Finnish Construction Trade Union plans to support paper workers with a sympathy strike.
The strike begins on Tuesday morning and will continue as long as the employers' lockout in the paper and pulp industry.
The construction workers' action will cover all plants that have been closed by the lockout or are involved with it.
The Federation of Special Service and Clerical Employees had earlier decided that its members would stop processing any import or export documents of the Forest Industries Federation or its members.
Several trade unions have said they will meet this week to decide on what action to take against the paper workers' employers.