Green Party sport spokeswoman Alison Johnstone said fans' trusts were "most likely to be the most responsible and most successful owners for their clubs in the long term".
She added that clubs such as footballing giants Bayern Munich in Germany showed how well fan ownership could work.
The Green Party wants the right-to-buy principle that was established during rural land reforms to be extended to help supporters of football clubs to buy them
The Scottish Government's Community Empowerment (Scotland) Bill already sets out plans to expand the community right to buy, with Ms Johnstone bringing forward amendments to the Bill.
One amendment she is proposing would extend the scope of the Bill beyond land and physical assets, to include clubs' membership shares.
The party also plans measures to empower fans' trusts, including giving them the first right of refusal if their club comes up for sale, and making them eligible for funding support from the Scottish Government
Fans' trusts should also be able to buy a proportion of the shares in a club, if they cannot afford the full value, the Greens propose.
Ms Johnstone said: "Too many Scottish football fans have gone through painful cycles of boom and bust at their clubs, where irresponsible owners run up unsustainable debts in the pursuit of short-term glory, or even simply fail to pay their taxes.
"Hearts, Rangers and Dunfermline supporters are just the most recent to have been put through the wringer. Quite simply, enough is enough."
The Lothian MSP said: "Greens believe fans' trusts are most likely to be the most responsible and successful owners for their clubs in the long term, and they should not be treated just like any other buyer for a club. The international examples such as Bayern Munich and Malmo show how well fan ownership can work, just as it already does at Scottish clubs including Clyde FC and Stirling Albion."
While she said the Community Empowerment Bill was "headed in the right direction", she added that it "should go further".
She added: "We know these plans are ambitious, but we hope to secure Scottish Government support for the principle of fan ownership, and we will seek to work with ministers to ensure the most practical and effective legislation possible."
Supporters Direct Scotland, which promotes fans' involvement and community ownership for clubs, welcomed the proposals.
Paul Goodwin, the group's head, said: "Community and fan ownership must not be seen simply as a last resort; but as a viable and sustainable route for clubs to adopt. There are of course recent high-profile, and impressive, examples of supporters and communities coming together effectively to save their clubs at a time of extreme difficulty, but those are not the only circumstances when fan ownership is appropriate.
"There are many other clubs who have either moved into, or are progressing towards, a model of increased community and fan involvement in their clubs without the spectre of doom staring them in the face. At this time we are working with Annan Athletic, Ayr United and Motherwell, which demonstrates what we believe to be a new dawn for Scottish football. As we can see in different parts of the world, this model can bring real and positive change to a club and to the communities they are part of."