The Government has been given four months to decide whether to hold a referendum on overhauling its voting system.
Non-members of the Oireachtas could be eligible for a job as a minister under potential reforms, which will be up for debate until December 27.
A spokesman for the Constitutional Convention, which published a report on recommendations made by its 100 members, said if the Government agrees, a public vote could be held 12 months from now.
"The Government has four months to respond by way of debate in the Oireachtas, to discuss the recommendations and to agree on whether to change the Constitution," the spokesman said.
"If it so decides, it will have to set a new timeline for a referendum, which will happen during the lifetime of this Government.
"That could be as soon as the third quarter of 2014."
The Constitutional Convention published a report on its fourth plenary meeting on electoral reform, which was held over two weekends in May and June.
Members, who were asked to vote on a string of reforms, indicated overall changes should be made.
More than half (55%) said non-members of the Oireachtas should be allowed to be appointed as a Government minister.
Some 59% said Dail members should have to resign their seats when they become a minister.
The convention was also in broad favour of making changes to improve voter turnout - with 97% favouring the establishment of an electoral commission, 89% supporting extended polling hours, 91% in favour of greater access to postal voting, and 100% voting to improve the accuracy of the electoral register.
Overhauling the current proportional representation single transferable vote system was also recommended.
More than half (54%) agreed the system should be changed, but almost four-fifths (79%) rejected replacing it with a New Zealand or German-style mixed-member proportional representation system.
A large majority voted for the introduction of larger constituencies, with 86% in favour.
More than two-thirds also supported changing the alphabetical order of political candidates on ballot papers.
The convention spokesman said the Government had given "an assurance of action" on the recommendations, which means it has from now until December 27 to consider them.
"The wheels of Government will now start turning," he said.
"Various people will start looking at it in different departments, memos will be sent to Cabinet, time slots will be allotted for Cabinet to discuss whether they think the proposals are a good idea, whether they merit a referendum.
"There is no obligation for the Government to hold a referendum. All they are bound to do is to hold a debate."
The next meeting of the Constitutional Convention will be held on September 26 and 27, when members will vote on whether Irish citizens abroad should be allowed to vote in certain elections.
The convention was formed to be representative of Irish society and parliamentarians, with independent chairman Tom Arnold.
Former justice minister and attorney general Michael McDowell claimed there was "complete inconsistency" between the Government's promise to consider the Constitutional Convention's recommendations and its move to abolish the Seanad.
Mr McDowell, who has campaigned for a No vote in the forthcoming referendum on the scrapping of the upper house, said voting for its abolition would mean voting to end the possibility of non-TDs becoming ministers.
"On the one hand, the Government has solemnly undertaken to consider any recommendations from the Constitutional Convention, including the recommendation that non-TDs should be eligible to be made ministers," he said.
"At the same time, the Government is asking the people to vote to make this impossible. In effect, the Government is now saying, 'Vote to change the Constitution now to make it impossible to appoint non-TDs as ministers and we will consider between now and Christmas asking you to reverse that decision in a referendum next year'."