Mr Ghani was speaking after the Taliban released an audio tape said to be from Mullah Mansour in which he calls reports of the firefight "baseless".
It was said to have taken place near the Pakistani city of Quetta last week.
Mansour was declared leader in July after the Taliban confirmed that Mullah Omar had died in 2013.
Mansour's appointment then prompted splits in the Taliban.
Read more
Mr Ghani told a press conference on Monday:  "There is no evidence that Mansour has been killed."
He added: "The incident that occurred should be carefully analysed."
He was referring to a gunfight that was said to have taken place on the outskirts of the western city of Quetta last Tuesday.
Some reports said Mansour had been seriously hurt, others that he had died, along with four Taliban gunmen.
Late on Saturday, the Taliban released the audio tape in which the speaker refers to the "rumour that fighting happened among the Taliban at a time when a meeting was in progress".
"The rumour says I was injured during the clash and later some media outlets reported that I died. Brothers, this report is not true, there is no doubt that it is enemy propaganda," the speaker says.
The voice resembled that in previous recordings issued by Mansour but there has still been speculation about its authenticity.
In the 17-minute message he says he has not seen the place where the fight was said to have taken place "for years", adding: "I am safe and my colleagues are safe. I am among my colleagues."
The speaker insists the Taliban will continue to fight to establish an "Islamic government" in Afghanistan and resist peace overtures.
Since August Mansour has overseen a series of battlefield victories, including briefly capturing the northern Afghan city of Kunduz.
But the movement has split into openly warring factions.
A number of senior Taliban commanders refused to pledge allegiance to Mansour and a faction opposed to him was set up last month under Mullah Mohammad Rasool.
Afghan President Ashraf Ghani says there is "no evidence" Taliban leader Mullah Akhtar Mansour is dead, after reports of an internal gunfight.