Abdelaziz Bouteflika has been in power since 1999.
Algeria's government has proposed a constitutional change that would open the way for President Abdelaziz Bouteflika to run for a third term.
Algeria's constitution currently includes a two-term presidential limit. Mr Bouteflika's second term is due to end in April next year.
He is widely expected to run for a third term in office, though he has not publicly confirmed that he will do so.
Opposition parties have criticised the move as a threat to democracy.
Parliament, where the president's supporters enjoy a large majority, is expected to approve the long-awaited constitutional change in the coming weeks.
"The amendment proposed to article 74 of the constitution maintains that the duration of the presidential mandate is five years and stipulates that the president of the republic can be re-elected," the official APS news agency reported.
The current constitution says the president can be re-elected "only once" - words that would be dropped from the amended text.
Mr Bouteflika, 71, has served as president since 1999.
He has overseen a reconstruction and development effort following a brutal civil conflict that began in the 1990s and cost more than 150,000 lives.
Last week, the president said the constitutional changes would "permit the people to exercise their legitimate right to choose their rulers and to renew their confidence in all sovereignty".
But opposition parties said the changes served only to increase the power of the president and his "clan", and that they should be put to referendum.
The constitutional amendment would provide for several other changes, including one that would allow the president to name one or several deputy prime ministers.