During a media round, Transport Secretary Grant Shapps was questioned over how Mr Sunak responded to lobbying by former prime minister David Cameron to try to get access for the company to a financial scheme during the pandemic.
Mr Shapps told BBC Radio 4’s Today programme: “The rules are crystal clear. What you must do is let officials know about whatever has happened, that you can’t help somebody contacting you, and you simply forward that on.
“That is the right approach … that decision is then made by the Civil Service machine. In this particular case, the request was turned down.”
He denied there was any “impropriety” in the way the Chancellor had behaved.
However, Labour has called for an investigation into the affair after Mr Sunak revealed he “pushed” officials to consider plans that could have helped Greensill.
Labour also questioned whether the Chancellor may have broken the ministerial code.
Mr Sunak yesterday published two text messages he sent to Mr Cameron in April 2020, although messages sent by the former prime minister have been withheld by the Government.
Greensill had approached Treasury officials regarding access to the Covid Corporate Finance Facility.
Greensill subsequently filed for insolvency, putting at risk thousands of steelmaking jobs in the UK.