A board paper by NHS Lanarkshire warns that steps must be taken "urgently" to increase capacity at the Beatson.
Radiotherapy services for patients across the West of Scotland are currently solely provided by the world-leading cancer centre at Gartnavel hospital.
Four health boards have voiced support for a new £24million jointly funded satellite service to ease pressure on the Beatson.
It is the UK's busiest radiotherapy centre and is operating at close to maximum capacity.
The Beatson takes referrals from NHS Greater Glasgow and Clyde, Lanarkshire, Ayrshire and Arran and Forth Valley.
Radiotherapy works by destroying cancer cells in the area that is treated.
It can cure some cancers and reduce the chance of a cancer coming back after surgery. It may also be used to control a cancer or to help improve the symptoms.
The Scottish Government has pledged to increase by 25% the number of patients diagnosed in the first stage of cancer, which will increase demand for services.
Focusing on the three most prevalent cancers, lung, breast and bowel, the programme aims to diagnose an additional 500 patients nationally with early stage cancer.
Cancer rates are also expected to rise with an increasingly ageing population.
The favoured site for the new radiotherapy service is Monklands hospital in Airdrie because it has 24-hour A&E services, provides chemotherapy for four of the main cancers, breast, lung, bowel and prostate and is considered accessible for the majority of patients. New CT and MRI scanners are also due to be installed.
If approved, construction would start in February next year with the service opening in late 2015.
The board papers state the Beatson's level of activity is "unsustainable".
It adds: "Steps need to be taken to increase the available capacity for the West of Scotland population.
"In addition to the currently high levels of demand, there is also a documented projected increase in incidence of cancer in line with an ageing population.
"The West of Scotland Regional Planning Group considered that a proposal for a satellite radiotherapy facility should be progressed as urgently as possible."
A spokeswoman for NHS Greater Glasgow and Clyde said: "Following the Scottish Government's work to look at cancer prevalence across Scotland, beyond 2015, West of Scotland Health Boards have been developing proposals to increase the number of radio-therapy machines available.
"These additional linear accelerators would operate as a satellite facility for the Beatson West of Scotland Cancer Centre, increasing existing capacity and allowing more patients from across the West of Scotland to be treated closer to home.
"Work has only recently started to explore the possibility of developing the new radiotherapy facility.
"Plans are at an early stage and work will be carried out over the next few months to explore a number of potential options in more detail."