The cash would upgrade in-patient wards, expand the day case area for chemotherapy and buy extra equipment to meet increased demand for radiotherapy.
A brand new £300m cancer centre for the whole South East of Scotland is due to be built at the Western once some other services are relocated to the Edinburgh Royal Infirmary site at Little France from next year.
But the earliest completion date for the new centre is 2025 and NHS Lothian says the existing premises require investment to bring them up to modern standards in the meantime.
Two wards need upgraded to bring them into line with guidelines on matters such as the space patients have around their beds and the provision of wash-hand basins.
Lothian Conservative MSP Miles Briggs has raised the cash plea for the Western in the Scottish Parliament and Health Secretary Shona Robison has agreed to meet him and other Lothian MSPs.
Mr Briggs said he looked forward to a new world-leading cancer centre at the Western.
But he said: “The current building is not fit for purpose. It’s quite clear it’s beyond its life expectancy. A lot of people love it because of the work it does, but it’s not the modern space patients are entitled to expect.”
An NHS Lothian spokeswoman said it was estimated cases of cancer would increase by 20 per cent by the end of the decade. “Our aim is to build a new South East Scotland Cancer Centre on the Western General site.
“This is an exciting plan which will see significant investment to create a new centre of excellence for cancer care – closely linked to the latest medical research and developments.
“Developing this will take time and there is a need for more immediate investment in our current facilities to ensure we can continue to meet the needs of patients while plans for the new building are being developed.”
Ms Robison told Mr Briggs in parliament that any new investment in the cancer centre by the Scottish Government would need to be looked at in the context of the bigger project.
A government spokeswoman said: “The Scottish Government recognises the importance of providing high quality cancer services at the Edinburgh Cancer Centre and are supportive of NHS Lothian’s plans to develop a business case.
“A decision on the funding will be made following review of the business case and it would not be appropriate to make any decision before that review is complete.”