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.
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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.

The Pass Wide and Slow Wales campaign has collected 1,300 signatures on the assembly's e-petition website.
It wants an annual road safety awareness campaign explaining to motorists how to react around horses.
The British Horse Society found that since 2010 there have been 2,000 road accidents in the UK, with 1,500 because of cars passing too closely.
As a result of these, 180 horses and 36 riders have died.
Awareness rides were planned for Penarth, Vale of Glamorgan, Swansea, Neyland in Pembrokeshire, Machynlleth, Powys, Flintshire and Porthmadog in Gwynedd.
Any petition with over 50 signatures is considered by a committee to be debated in the assembly.

Councillors are unhappy Ordnance Survey (OS) maps only refer to Black Rock Sands near Porthmadog by that name.
But it is also know locally as Traeth Morfa Bychan - after the village next to the shoreline.
OS told the authority the name was adopted after consultation with the council, and they had been told the English version was most commonly used.
"During the council's Language Committee, members declared their commitment to protecting indigenous Welsh names and places in Gwynedd," said a council spokesperson.
They said they would continue to collaborate with agencies such as OS to "ensure that the correct names are used wherever possible".
"In this case, the discussion with the OS will continue regarding the possibilities for changing the name that appears on their maps," added the Gwynedd official.
"In the meantime Gwynedd council will consult with community councils in the specific area, to gather evidence that will enable the council to submit robust evidence to the OS for changing the name that appears on their maps."

19 April 2017 Last updated at 17:21 BST
So who's in and what's it all about? Here's the lowdown...
Afghan Taliban leader Mullah Akhtar Mansour has been seriously wounded in shooting at a meeting of militants in Pakistan, Taliban sources say.
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Awareness rides are taking place to try and cut the number of people on horseback injured or killed on roads.
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Officials have said they will push to get the Welsh name of a Gwynedd beach on maps.
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The squad for the British and Irish Lions tour has been announced.