The two sides will play at the Stadio Olimpico in Rome in the first ever Rome derby cup final, which is provisionally scheduled for 1845 GMT on Sunday May 26.
However, fears about the violence that often surrounds the fixture has sparked calls for the match to be moved from the evening.
"Kickoff times can sometimes help to draw attention to less attractive games, but the derby doesn't need that and can be moved to a time that makes it more manageable," Italian news agency Ansa quoted Alemanno as saying on Friday.
"After the election of the president of the republic, I will decide whether to make a formal request to Serie A, the government and local police authorities."
Roma and Lazio drew 1-1 in Serie A on the evening of April 8 and there were violent scenes before and after the match with several people stabbed as hardcore 'ultrà' supporters from both sides clashed among themselves and with police.
About 200 Lazio fans threw bottles and other objects at officers who responded by firing tear gas and baton-charging supporters.
There have been calls for derbies never to be played in the evening again after local residents complained they were terrorised by "civil war".
The Cup final situation is complicated by the Rome mayoral elections that will take place on the Sunday, meaning an afternoon kickoff could affect voting.
However, moving the game to the day before would mean it could clash with the buildup to the Champions League final in London.
Next week Italian football authorities are set to meet and decide whether to keep the current kickoff time, while Rome's head of police Fulvio Della Rocca has called for calm especially among the media.
"If today we're already seeing headlines in the papers about a city in lockdown and the risk of fighting, then tension is being ramped up, for which there is no need," he said.
"For this match there has to be the involvement of civil society as well as the police to make the match a big party. We all have to co-operate."