Chair of the NSW parliament upper house committee, Greens MP Cate Faehrmann, said the staffers have been sent invitations to an upper house inquiry into the hiring next Tuesday.

Also invited was General Counsel of the Department of Enterprise, Trade and Investment Chris Carr.

Meanwhile, testimony given by former public servant Jenny West on Monday about Mr Barilaro's appointment as the state's Senior Trade and Investment Commissioner to the Americas has been sent to the NSW Independent Commission Against Corruption.

Ms West, a former deputy secretary for Investment NSW, told the inquiry she was the successful candidate for the role in August, before her offer was rescinded.

She said Investment NSW CEO Amy Brown later said the job would become a "present for someone".

The committee investigating the appointment agreed it should be referred to ICAC, Ms Faehrmann told AAP.

"The committee was particularly concerned at Ms West's evidence that the role was being given as a 'present' to someone else," Ms Faehrmann said in a statement.

"The public demands that public service roles, funded by the taxpayer dollar, be recruited with the highest level of integrity.

"It is clear that this has not been the case in this situation."

An ICAC spokeswoman told AAP "the commission cannot confirm or deny if it has received referrals, or whether it is considering or undertaking investigations".

The position was formally given to Mr Barilaro last month.

Ms West told the inquiry she felt "so confused" and "shocked" when Ms Brown told her she no longer had the New York job and would also be made redundant from her position.

Ms West's testimony conflicts with statements made by Ms Brown, who told the inquiry she withdrew the offer after the relationship became "irreconcilable" between Ms West and the government.

Mr Barilaro, the former Nationals leader, resigned from parliament last year and was named in mid-June as the successful candidate, before withdrawing two weeks later amid a political storm.

Premier Dominic Perrottet said reports coming out of the inquiry are worrying.

"There is absolutely no place for gifts of government jobs, whether they are statutory appointments or whether they are government sector appointments," he told reporters on Tuesday.

He said a second review he launched into the appointment was expected to report back within weeks.

"I will make that public and I will immediately respond to any of the recommendations," the premier said.

"Obviously yesterday, the reports are concerning and from my perspective, this independent review will look at that."

Labor leader Chris Minns said the inquiry had unearthed that a "perfectly qualified, educated and experienced woman" had been entirely qualified for the job.

"It's now incumbent on the premier of NSW to explain what the hell has happened here," Mr Minns said.

He called on Mr Perrottet to clean up prior statements claiming the process was independent, and no successful candidate had been found.

"The premier needs to ... correct the record today and explain why he misled the New South Wales parliament," he said.

"If it was unintentional, he needs to explain that to the people of NSW."

Trade Minister Stuart Ayres issued a statement on Monday rejecting any suggestion he exerted political influence on the recruitment process, saying Ms Brown was the decision-maker for the role.

"I did not say the job was to be a 'present' for anyone and I find that idea to be offensive," he said.

Australian Associated Press