The enlarged gold mining company came into effect last week following its all-share merger with the Bristow-founded Randgold Resources.
Bristow declined to discuss details with the Wall Street Journal about the negotiations in Tanzania, where Barrick subsidiary Acacia Mining was hit with a US$190 tax bill in 2017 and has been banned from exporting gold concentrate.
However, he told the newspaper: "We will find a solution.
"This can't continue, every stakeholder is hurting."
Bristow also expects to unveil "a number of strategic changes" in February.
He told the WSJ the company was reviewing the possible sale of its 50% stake in Kalgoorlie Consolidated Gold Mines, the Hemlo gold mine in Canada and Lagunas Norte in Peru.
He also said he planned to shrink Barrick's head office from a team of nearly 200 to about 60 people.
In a joint statement last week, Bristow and Barrick executive chairman John Thornton said the company would optimise its existing operations, pursue new opportunities that met strict investment criteria and develop them with "disciplined efficiency".