Momis, from Buin in South Bougainville, has already served two five-year terms as president - from 2010 to 2020, The National newspaper reported.
Momis filed a case in the Supreme Court this year arguing that the provisions in the Bougainville Constitution on the matter was not consistent with the PNG Constitution and should be declared unconstitutional, The National newspaper reported.
His lawyer Loani Henao submitted that the Bougainville Constitution was "subject to the PNG Constitution", and therefore should give people the "right to vote and stand for public office".
Solicitor-General Tauvasa Tanuvasa representing the Justice Minister and Attorney-General Davis Steven told the court the matter was for the Bougainville House of Representatives to legislate on.
Speaker of the Bougainville House of Representatives Simon Pentanu through lawyer Greg Sheppard argued that the court should decline to give an opinion as the operation of the Bougainville Constitution should be left to the House of Representatives to determine.
Four of the five judges - Chief Justice Gibbs Salika, Deputy Chief Justice Ambeng Kandakasi, Justice Nicholas Kirriworm and Justice David Cannings ruled that the provisions were constitutional and valid as to how Bougainville decided on the election of the president by its parliament.
Justice Kandakasi said the Bougainville Constitution "is the law when it comes to matters that are exclusive to or only applicable to Bougainville". Justice Les Gavara-Nanu ruled otherwise, saying the provisions referred to by Momis were inconsistent with the National Constitution, The National reported.