The proposal - effective from 2020 when the current term of incumbent Maithripala Sirisena ends - was presented by the President himself.
The new system will transfer more executive powers to the Prime Minister.
Sirisena, who succeeded Rajapaksa after the January polls, had pledged to abolish the presidential system in order to empower parliament.
Foreign Minister Mangala Samaraweera said a Cabinet sub committee has been appointed to make the necessary recommendations.
In 2010, Rajapaksa secured the Parliament's nod to remove presidential term limits from the Constitution through an amendment that also included provisions with more far-reaching implications - by increasing the president's power to act without oversight.