Jones told the Herald today he hoped to raise the issue with State Services Minister Chris Hipkins next week.
But PSA's national secretaries, Glenn Barclay and Erin Polaczuk, say Jones' measures would undermine public servants' constitutional role.
"They need to be free, frank and fearless – not controlled, cowed and cronyistic," they said in a joint statement.
They also said Jones' comments were reminiscent of the previous Government's "attacks on public servants."
"Our members do their jobs with commitment and integrity – despite increasing workloads, unending restructuring and a meaningless staffing cap."
New Zealand was rated top of Transparency International's list of the least corrupt countries in the world.
"Cronyism and political interference would severely damage that reputation."
"If Mr Jones is concerned about delays, then he needs to direct his considerable energies towards influencing the Government to lift the cap on public service staffing.
"And while he is at it he should push For the Government to relax the budget responsibility rules so the damage of nine years of underfunding can be repaired, and real change being."
For the past 30 years, top public servants have been appointed by and are employed by the State Services Commission - although the Government of the day can veto a recommended appointment.
The PSA says that in New Zealand, core Government administration makes up just 12.39 per cent of total employment compared with 18.98 per cent in Canada and 23.4 per cent in Britain.
Jones, a New Zealand First minister in the six-month old Government, has been criticised in the past For deviating from well-established norms when he criticised the board of Air New Zealand For cutting flights to Kapiti.
He has sought to find a way around that by saying today that his proposal to change the way the top echelons of the public service are appointed is being made in his capacity as a New Zealand MP and will be taking it to his party's conference.