According to the BBC, the offer is to be made as part of plans which will also expand the role of firefighters and see them assume responsibility in areas such as tackling terrorism and providing emergency medical care.
It is also expected that between 200 and 300 jobs could be cut.
Staff have yet to receive the offer, which is due to be discussed by the Scottish and UK Fire Brigade Union next week.
A Scottish Government spokesman said the Scottish Fire and Rescue Service (SFRS) had made clear there would be no compulsory redundancies as part of the plans.
He said: “Operational decisions on the allocation of resources are a matter for the SFRS board and chief officer, who have been exploring for some time now how best to develop the service to meet new and emerging risks, including how transformation could see SFRS do more for the people of Scotland.
“The process involves liaison with staff, partners and the public.
“The SFRS has indicated that their proposed reward package would be for a new, expanded role for firefighters, which, of course, is still to be negotiated and agreed with unions.”
He said the government had provided extra funding for the fire service.
“Much progress has been made through fire reform, improving outcomes and access to specialist facilities while protecting frontline services and keeping people safe,” he added.
“In the draft budget, we have increased spending capacity of SFRS by £15.5m for 2018-19, providing £5.5m extra and ensuring they keep £10m in full from VAT costs, to invest in transformation plans.
“This is on top of the £21.7 million increase in the operational budget for the fire and rescue service this year to support investment in equipment and resources.”
Kirsty Darwent, chair of the Board of the Scottish Fire and Rescue Service, said: “This Service has set out very clearly how it needs to transform to meet the significant new and emerging risks that Scotland now faces, such as severe weather-related flooding and terror attack.
“We are offering to pay our firefighters more - but we are asking them to do a lot more, by taking on a completely new role to enhance the safety of the communities they serve.
“This is a proposal. We will now enter into formal negotiations with staff and unions, and believe we can reach the right outcome for our firefighters and the people of Scotland.”