The consultation has been launched for the proposed Organ And Tissue Donation (Scotland) Bill, put forward by Glasgow MSP Anne McTaggart, calling for the change.
If the Bill is successful, it would mean, for the first time, the Scottish public would be able to register whether they would like to donate organs after death or 'opt out' of the system.
About 200 people have already responded to the consultation, with more than 90% of replies in favour of the proposals, which were launched in support of the Evening Times' Opt For Life campaign.
Major charities, including the British Heart Foundation, believe under an opt-out system the wishes of the individual are more likely to be known and respected by family members.
The findings reflect previous studies indicating that when the concept of opt-out is explained the majority of people are supportive.
Ms McTaggart is planning to have talks with Jo-Anne Dobson from the Northern Irish Assembly, who is attempting to bring through an Organ Donation Bill in Northern Ireland.
An opt-out system is due to come into force in Wales in December next year. It was influenced by evidence that suggested an opt-out system could increase the number of organ donors by 25-30%.
The Scottish consultation is due to close on September 25, after which the responses will be analysed.
Ms McTaggart said: "I have received well over 200 responses to my proposal and the vast majority of these have been positive.
"About 90% of respondents have expressed support for adopting an opt-out system of organ donation, which reflects the findings of previous public attitude surveys on this issue.
"I am confident we can achieve the same result in Scotland as achieved in Wales. I want to do this by proving this change is supported by a significant majority of people living in Scotland.
"I encourage everyone to respond to my consultation, whatever their views on the issue, and to share this proposal with friends and family.
"Only by creating an open dialogue on the subject of organ donation can we truly be sure of the wishes of our loved ones.
"I am hopeful this will result in more lives being saved by organ donation."
Marjory Burns, Scotland director with BHF Scotland, said the charity fully supported the Bill.
She said: "We are delighted to see the people of Scotland engaging in the consultation and would encourage everyone to have their say.
"Three people a day die across the UK because they are in need of an organ transplant and it is important we have this national conversation."
To take part in the consultation, see the website: www.annemctaggart.co.uk