Prime Minister Scott Morrison is also refusing to say whether the minister should go.

Mr Morrison confirmed on Thursday he had dinner with Treasurer Josh Frydenberg and Deputy Prime Minister Michael McCormack on Wednesday but said Senator McKenzie's future wasn't discussed.

Earlier, there had been speculation Senator McKenzie would resign or be pushed out by Friday.

However Senator McKenzie's office strongly denied that was the case.

Mr Morrison would not comment on Senator McKenzie's future until an investigation by Prime Minister and Cabinet secretary Phil Gaetjens was finalised.

Mr Gaetjens - who is Mr Morrison's former chief-of-staff - will determine whether Senator McKenzie breached ministerial standards through her use of the program to give a $36,000 grant to a shooting club that had gifted her membership.

"It's the right thing for me to do to seek advice on those matters, I await that advice and I await that report," Mr Morrison said.

Mr Morrison also played down reports his office had been involved in determining where grants went.

He said it was "the normal course of events" for MPs to lobby for money for their constituents.

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Mr Morrison also said he only revealed the investigation on Wednesday due to media questions.

The Canberra Times asked his office on Tuesday whether the matter would be referred to Mr Gaetjens. It failed to respond.

Labor has been calling for Senator McKenzie's scalp since last Thursday, after the Australian Auditor-General found Senator McKenzie's office made up its own rules for doling out sporting grants.

It also found the Minister possibly did not have the legal authority to be making the final decisions on where grants went.

Labor's sport spokesman Don Farrell described it as "pork barrelling on an industrial scale".

Nationals leader Michael McCormack and Prime Minister Scott Morrison have indicated they are standing by Senator McKenzie.