The report by the Frontier Post came after a trilateral summit in Ankara earlier this month between Afghanistan, Pakistan and Turkey.
But the Turkish foreign ministry denied the report, saying it "does not reflect the truth". "No such office has been opened in Turkey."
The Frontier Post also said Pakistan's top intelligence officials had met with the political advisor of the Taliban's supreme leader Mullah Omar in Ankara.
Turkey has said in the past that it was open to the establishment of an office for the Taliban to help with peace talks with Afghanistan.
The Western-funded Kabul government is trying to strike a peace deal with the Taliban before the withdrawal of foreign troops by the end of this year but the process has stalled.