Top surgeons say the country's first lung transplant programme should be carried out in the Clydebank hospital to help more Scottish patients.
Currently, all people from Scotland who are to get a lung transplant must travel to the Freeman Hospital in Newcastle.
The calls to use the Golden Jubilee came during a conference in Glasgow on organ donation, organised by the Scotland Patients' Association, where more support was gathered for the Evening Times' Opt For Life campaign.
Saleem Haj-yahia, lead heart transplant surgeon at the hospital, said he thought Scots patients would get a better deal if the Golden Jubilee carried out lung transplants.
He said: "It takes three or four hours to get to Newcastle. If someone needs a transplant they usually need it immediately so it would be better for these people if there was a transplant programme in Scotland.
"We already have the infrastructure in the Golden Jubilee because we do heart transplants, so it would be cost-effective. We hope it will come about by 2014 or 2015."
Medical experts and transplant patients said they supported the Evening Times' campaign for Scotland to move to a system of presumed consent for organ donations – known as an opt-out system – rather than the current opt-in.
It came after the Evening Times revealed yesterday Scottish Labour had become the first political party to publicly back our campaign.
Public Health Minister Michael Matheson told the Glasgow conference Scotland had met its target of increasing the number of donors by 50% a year early and said the Scottish Government would consider moving to presumed consent next year.
He said: "Scotland now has the highest percentage of population on the organ donor register in the UK.
"When the taskforce's recommendations were made we said they would be reviewed in 2013 – this work will consider all issues relevant to organ donation, including opt-out."
Marc Clancy, a consultant transplant surgeon at the city's Western Infirmary, said a move by Wales to an opt-out system could pave the way for Scotland.
He said he supported presumed consent because it would let medics preserve organs so they did not go to waste if someone died suddenly.
Transplant survivors also backed our campaign.
Errol Burchell, 70, from Lenzie, was given a new liver 18 months ago at the Scottish Liver Transplant Unit in Edinburgh Royal Infirmary.
He said: "I cannot say in words how thankful I am for my gift of life, so I support the opt-out campaign."
HOW YOU CAN HELP
WE need your help to make this happen and save more lives. Sign our petition to lend your support to an 'opt-out' system for organ donation at: www.eveningtimes.co.uk
There is also a printable version of the petition available on our website.
We already have more than 10,000 signatures but want thousands more. So we need as many of you as possible to distribute it in community centres, churches, mosques, leisure centres and public places.
You can also sign up on Twitter and Facebook via http://bit.ly/etoptin. Don't forget to send the link to as many friends as possible.
To join the existing national organ donor register, text 'ETDONATE' to 61611.
Texts are charged at the usual standard network rate (any texts sent in reply are free to the recipient).
You can also join the list by calling the NHS Donor Line on 0300 1232323. Lines are open 24 hours a day. Calls are charged at your contracted rate for local calls.
Those who wish to register online can also do so by filling out a form on: www.organdonation scotland.org/ nhs_organ_ donor_ register. html