Four Taliban gunmen were killed in the gunfight after an argument on the outskirts of Quetta, a source said.
Another report said Mullah Mansour died but this is unconfirmed. A Taliban spokesman denied the gunfight happened.
Mullah Mansour’s appointment prompted splits in the Taliban after its founder Mullah Omar’s death emerged in July.
A number of senior Taliban commanders refused to pledge allegiance to him and a faction opposed to him was set up last month under Mullah Mohammad Rasool.
The Taliban source said the firing seemed to be spontaneous rather than planned.
Several other Taliban sources told the BBC that Mullah Mansour and his bodyguards had been at the house of another militant, Abdullah Sarhadi, when fighting broke out.
Sarhadi is a Taliban figure with symbolic importance after spending years in US detention in Guantanamo Bay, reports the BBC’s Dawood Azami.
Compared to Mullah Omar, his secretive predecessor, Mullah Mansour has adopted an open approach and has met Taliban commanders regularly to discuss their policy concerns, our correspondent says.
What prompted the shooting in Quetta is unclear.
“During the discussion, some senior people developed differences and they opened fire at each other,” said a senior Taliban commander, Reuters reports.
Taliban spokesman Zabihullah Mujahid categorically rejected the reports.
“No such incident has happened, because he is in Afghanistan not in the area of Pakistan they have mentioned. Secondly his security is not weak to allow such an incident,” he told the BBC Afghan service.
Mullah Omar died in 2013 but his death was only confirmed in July.
News of his death disrupted fledgling peace talks between the Afghan government and the Taliban.
Some senior Taliban leaders had been suspicious of Mullah Mansour’s support for peace talks hosted by neighbouring Pakistan, and accused pro-Pakistani circles of installing him as the new leader.
Since August Mullah Mansour has overseen a series of battlefield victories, including briefly capturing the northern Afghan city of Kunduz – a huge setback for Western-backed Afghan forces.
But the Islamist movement has split into openly warring factions since Mullah Omar died.
Recent reports suggest one of the leaders of the breakaway Taliban faction, Mullah Dadullah, was killed in recent fighting with militants loyal to Mullah Mansour.