The party pledged to support the Scottish Crown Estate Bill in its stage one debate at the Holyrood on Tuesday but said they plan to made sweeping changes at a later stage.
The Crown Estate Scotland comprises assets and rights owned by the monarchy including harbours, coastlines and forestry.
Around half the foreshore in Scotland is under the organisation’s ownership, and its assets were valued at around £275 million in 2017.
The Smith Commission in 2014 recommended devolving management and revenues to Holyrood, with management then further devolved to local authorities.
The 2016 Scotland Act devolved the management and revenues are now paid into the Scottish Consolidated Fund but control over revenues was not devolved.
The Scottish Crown Estate Bill, introduced to Holyrood in January, aims to reform Crown Estate management and enable transfer of management to other bodies within a national framework.
Amendments the Greens are considering tabling at the Bill’s second stage include abolishing the Crown’s rights to the foreshore and transferring this to local authorities.
Andy Wightman, the party’s land reform spokesman, said: “Communities the length and breadth of Scotland are routinely hampered in their efforts to make the most of historic assets such as harbours, foreshores and the seabed.
“To date the Crown Estate has been remote and unaccountable, and sadly it seems most parties at Holyrood are content with a business-as-usual approach to this feudal relic when it really needs a radical overhaul.
“Greens will continue to champion local accountability, and we will support the Bill at stage one, to allow it to proceed to the next stage of committee scrutiny.
“We will seek to amend it to bring about a modern system of asset management that puts local communities in charge.”
A Scottish Government spokeswoman said: “Scottish Ministers will consider the Green Party’s comments carefully, along with all other proposals.
“The reforms in the Bill have been designed to create significant opportunities, and we are committed to maximising the benefits of the Scottish Crown Estate for our communities and for Scotland, while ensuring assets are well maintained and managed, with high standards of openness and accountability.”