The inquiry is looking into the appointment of former NSW deputy prime minister John Barilaro to the US job.
Labor will try to get the inquiry's terms of references expanded and comes ahead of Mr Barilaro's appearance on Monday.
Reports were made in Nine newspapers that Prime Minister Dominic Perrottet had offered to create a new parliamentary trade role for Transport Minister David Elliott.
The Premier also claimed that he was removed from cabinet after manoeuvres that caused him to speak to Mr Elliott about the agent-general position in London. The allegations against the Premier were very serious, according to the leader of the Opposition in the upper house, Penny Sharpe.
The Premier can't hide behind an inquiry. This goes directly to his involvement and he needs to answer those questions straight away.
I can say today that we will be trying to expand the terms of reference of the inquiry to include all appointments for the senior Trade and Investment Commission, including the UK agent-general. Perrottet did not hold a press conference today, but the ABC put specific questions to his office, asking if he could create a parliamentary trade role or discuss the agent general position with David Elliott.
A statement from a spokesperson stated thatwhoever the Premier considers appointing to his ministry is a matter for the Premier alone. The same questions were put to David Elliott but were not directly addressed.
He said in a statement that he is committed to delivering the NSW government's infrastructure pipeline, which is helping transform our state, and ensuring that public transport delivers first-class services for the people of NSW.
I have no interest in working overseas. According to the opposition, the Premier has declined to appear before the inquiry but they say it's time for him to come clean. We would expect that he'd want to give information to the public, Ms Sharpe said.
It flies in the face of everything the Premier has said for the last seven weeks, that these are arm's length positions that have absolutely nothing to do with him.
I think that the Premier has said that it would be illegal for him to interfere in these matters. The debacle has been gaining momentum for weeks, and has prompted Barilaro to withdraw from the lucrative $500,000 a year New York-based job.
Trade Minister and Member for Penrith Stuart Ayres has resigned from his position as a leader in the party due to concerns about his role in the selection process.
A separate inquiry will take place into whether he broke the ministerial code of conduct, and Mr Ayres maintains that he did nothing wrong.
Barilaro will be in charge of the inquiry for the first time on Monday and is expected to face a heavy grilling.
Ms Sharpe said that the committee has many questions for him.
But clearly you want to understand his role in the creation of these positions, his role in the changing nature of the way in which these positions were appointed.
And any of the conversations he had with Minister Ayres or Mr Perrottet, or indeed anyone else in the government, when he applied for and was eventually offered that job. The chief executive of Investment NSW Amy Brown will join Mr Barilaro in giving evidence - it will be her third appearance before the committee.
During her testimony on Wednesday, August 3 she admitted that the appointment was not done at arm's length from the government.
A report on a separate review initiated by the Premier and conducted by senior public servant Graeme Head is expected to be published soon.
The upper house inquiry has conducted five hearings.