Erdoğan has been widely expected to seek the presidency in 2014, but only after introducing a presidential system form of governance through constitutional changes to replace the current parliamentary system headed by a prime minister.
Opponents fear such a system would further consolidate Erdoğan's dominance over Turkey without a parliament strong enough to rein him in. The current presidency is largely a ceremonial position, though the president must approve laws passed by parliament and makes important appointments in the judiciary and education.
From the early days of Gül's presidency there were doubts over whether he was subject to a five or seven year term, and the opposition wants the court to annul a law passed in January that said his term should end in 2014.
Should the court rule in the opposition's favour it would create uncertainty within the Justice and Development Party (AK Party) that Erdoğan dominates.
Erdoğan would have to seek the presidency this year, without the presidential system in place, or face a long delay until he could assume executive powers of a newly-styled presidency.
The court was set to begin deliberations on the presidential term, after first clearing other dossiers on Friday morning and it was unclear when a ruling could be expected. Journalists were not allowed into the courthouse.
If the court rejects the opposition petition, the presidential election will be held as planned in 2014, removing a source of political instability.
Uncertainty about the length of Gül's tenure has persisted since he was first elected by parliament on August 28, 2007 to a seven-year term despite fierce opposition from the secularist military over his Islamist pedigree.
In a referendum in October that year, Turks approved a constitutional reform package including a measure replacing the single seven-year presidential tenure with a renewable five-year term.
In a bid to clear up uncertainty over how long Gul would spend in office, parliament approved a law in January saying he would serve a single seven-year term. The opposition Republican People's Party (CHP) challenged the law as unconstitutional.
Under the 2007 reform package presidents will in future be elected by a popular vote rather than parliament.
Having overseen a decade of unprecedented prosperity in Turkey, Erdoğan is easily the most popular politician with the country's new, conservative-minded middle class, and he would almost certainly win any election, as the opposition is too fractured to mount a credible challenge.
But any move to the presidency could lead to jostling within the ruling AK Party, that would risk bringing factional rivalries to the surface.