A majority of Nigeria's 36 state governors have given their backing to moves to change the constitution.
Obasanjo has yet to say whether he would like to contest polls again
The most controversial part of the proposed changes is the scrapping of the two-term limit for elected officials, notably the president.
The issue has divided the ruling People's Democratic Party and Nigerian public opinion, with President Olusegun Obasanjo's second term ending in 2007.
Several governors did not attend the meeting and two walked out early.
Nigeria's powerful governors are also limited to two terms in office and so could benefit if the constitution were changed.
The chairman of the governors' forum, Akwa Ibom State Governor Obong Victor Attah, said it a constitutional review was necessary and should "be completed within the life of this administration".
The meeting also urged an end to the practice of regional meetings between leaders from either the south or the north of Nigeria.
They said such meetings could serve to divide Nigeria, between the Muslim majority north and the Christian and animist south.
Both northern and southern leaders have held meetings and demanded that the next president should come from their respective areas.
Mr Obasanjo has not publicly said he wants to stand for another term but there is increasing speculation that behind the scenes he is trying to secure a third term.
Supporters of Vice-President Atiku Abubakar oppose moves to change the constitution and he is thought to wish to succeed Mr Obasanjo.