Asked to confirm the rumours, Nabez Rashid Ahmad, the deputy director for the KDP Sulaymaniyah branch, replied: "He's in KDP-controlled land."
He gave his location as the Irbil region, but gave no details on when, where or how the purported surrender took place.
Ismail Sayer, an Iraqi opposition figure in the Democratic Platform of Iraq also said in a statement faxed from Sofia, Bulgaria, that Aziz had given himself up.
"Tariq Aziz has escaped from Baghdad to the north region," Sayer said in a statement.
However, the KDP spokesman in the northern city of Irbil, Fawzi Hariri, said: "We've heard the reports and we don't confirm them."