Mr Stanczak was abducted about 70km from Islamabad
Taleban militants in Pakistan say they have killed a Polish engineer kidnapped in September and have released a video purporting to show his death.
A Taleban spokesman said Piotr Stanczak had been killed after a deadline expired for the Pakistani government to free captured militants.
Polish Prime Minister Donald Tusk said Warsaw had received "informal confirmation" of the man's death.
Pakistani security officials said they could not confirm the Taleban claim.
A Taleban spokesman said Mr Stanczak had been beheaded after a deadline expired on Friday for the release of a number of militants in government hands.
"We have killed the man after authorities refused to release our colleagues," the spokesman, calling himself Mohammed, told Reuters news agency.
News agencies subsequently received copies of a graphic video apparently showing a man being beheaded.
Pakistani security officials said the Taleban wanted money for the return of Mr Stanczak's body.
He was kidnapped by gunmen on 28 September while visiting one of his company's sites at Attock in north-west Pakistan, about 70km (45 miles) west of the capital, Islamabad.
Mr Stanczak's company, Geofizyka Krakow, was doing surveying work for a Pakistani oil company.
His Pakistani driver, bodyguard and translator were killed in the attack.
The Pakistani government had been in negotiations with the Taleban for Mr Stanczak's release.
"From Pakistan we have an informal confirmation that this tragedy in fact took place," Mr Tusk told Poland's TVN24 news channel.
"We have used all political, operational, logistical means to prevent this tragedy," he said.
Piotr Adamkiewicz, a spokesman at the Polish embassy in Islamabad, said the mission had seen some images from the video.
"We are thinking that this is [Mr Stanczak] but we have to wait to receive the full tape," he told the Associated Press news agency.
Pakistan has been fighting a growing insurgency by Taleban militants in its north-west region bordering Afghanistan.
A number of foreigners have been kidnapped, including Afghan and Iranian diplomats and two Chinese engineers (one of whom later escaped).
An American official with the UN refugee agency based in Quetta, in western Pakistan, was kidnapped last week.