The cabinet approved a proposal to remove the two-term limit for presidents, which would mean Rajapakse could stand again when elections are scheduled in November 2016.
"The cabinet backed a move to amend the constitution," an official at the president's office said, declining to be named.
Rajapakse came to power in 2005 and won a second presidential term in January.
He has enough support in parliament to secure the two-thirds majority required to pass constitutional changes, but any amendment must also to be approved by the Supreme Court.
Several of Rajapakse's family hold key positions within the government, and the island's key aid donors, including the United States and Japan, have pushed him to enact political reform and to share power with minority ethnic Tamils.