"I do not exclude the possibility of this. If this appears in the constitution - the opportunity to run [for the presidency]. We will see," Putin said, as aired by Rossiya 1 TV channel.
The all-Russian vote on the amendments to the national constitution will be held on 1 July.
In late January, Mr Putin suggested amendments to the fundamental law, including reduction of the presidency to two terms and expanding the role of the legislature. The president also said that the State Council, currently an advisory body made up of regional governors, should have its status and duties fixed in the Constitution.