The fight over the drug, called Kadcyla, is being regarded as a test case after an overhaul of the system for ensuring patients can access the best new medicines in Scotland.
Nice, the decision-making body in England, has already indicated it wants to reject the treatment for health service use on the grounds of its cost.
However the charity Breakthrough Breast Cancer is calling for it to be given the green light north of the Border.
It is backed by Dr Iain MacPherson, an oncologist at the Beatson West of Scotland Cancer Centre, who has been involved in trials of the drug.
The treatment is initially intended for women who are seriously ill - patients whose cancer has spread and who have already stopped responding to another "landmark" drug known as Herceptin.
Trials have shown the drug extends patients' lives by an average of 5.8 months more than existing therapies and Dr MacPherson said there are patients in the West of Scotland who have been taking the treatment for around a year.
Kadcyla also stands out because it works by taking chemotherapy directly to cancer cells and has been found to spare women distressing side effects such as nausea, hair loss and a weakened immune system.
Dr MacPherson said: "From my point of view as a clinician treating breast-cancer patients I would like to see this drug approved. I think it is really quite a step forward for women with this type of breast cancer."
However, the medicine is reported to cost £6000 a month, and draft guidance from Nice says prescribing it for patients will cost tens of thousands more than existing alternatives.
Jenni Murray, presenter of Radio Four's Woman's Hour and a breast-cancer patient, has written an article saying she does not believe the NHS should fund it.
Breakthrough Breast Cancer in Scotland is calling on the Scottish Medicines Consortium (SMC), which advises what treatments should be given in Scotland, to work with maker Roche to find of way of making Kadcyla available.
James Jopling, Breakthrough Breast Cancer director for Scotland, said: "This drug is incredibly important because it is a targeted chemotherapy treatment.
"The side effects are less then other drugs we have seen from women with this particular type of secondary breast cancer and this will extend the time they have with friends, family and loved ones which we have not seen from other treatments."
A review of access to new drugs was launched after cancer specialists including consultants from the Beatson, told MSPs Scotland offered an "inferior health service", with patients being denied life-saving treatments available elsewhere in the UK.
Mr Jopling said the new SMC regime was meant to give patients a greater say, and Kadcyla will be a test of the system.