Prime Minister Theresa May is due to trigger Aricle 50 - formally serving notice of the intention to leave - this month.
The ManpowerGroup Employment Outlook Survey is based on responses from 2,119 UK employers and asks whether employers intend to hire additional workers or reduce the size of their workforce in the coming quarter.
The Outlook for the region is down one point to +5%, matching the national average.
Manpower Head of specialist markets Amanda White said: “Employment in the region has held fairly steady as we approach the triggering of Article 50.
“The region’s employers have recorded a slight fall in optimism, but we have seen much bigger falls elsewhere in the country.
“Despite the slight fall in optimism, the region has some real bright spots so job-seekers should be optimistic.
“Investment in infrastructure and new building projects in Newcastle and elsewhere in the region is fueling job creation in the construction sector, but skills shortages remain a huge problem.
“Bricklayers are in such high demand that they can earn more than £50,000 a year in the Tyne and Wear. Employers are reacting to the twin challenges of a skills shortage and an ageing workforce by providing more funding for apprenticeships.
“We’re seeing lots of new opportunities in the region’s call centres and employers are continuing to compete to find candidates for more technical roles.
“Jobseekers are increasingly reluctant to commute long distances, so employers are having to dig deep into local talent pools to find the people they need.
“Some employers are becoming more open to taking on staff with less relevant experience and offering on-the-job training.”
Nationally, private sector hiring has dropped to its weakest level since the first quarter of 2014.
Employers in six of the nine sectors surveyed reported a falling Outlook. The overall Net Employment Outlook, which includes both public and private sector employers, has dropped two points to +5%.
All but five regions report falling Outlooks for the coming three months.