The president's family hold key positions on the island, with three brothers taking the roles of defence secretary, Speaker of parliament and economic development minister. His son was also elected to parliament in April.
The cabinet endorsed the statute change on Wednesday, a spokesman for the government information department said.
"These proposals are to be brought before parliament as an urgent bill," he said, adding that the Supreme Court would be asked to decide on their constitutionality.
Rajapakse's second term ends in November 2016 and the existing laws prevent him from running for office again.
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His United People's Freedom Alliance won 144 seats in the 225-member parliament at April elections, but has the support of opposition defectors to secure the two-thirds majority n