The Daily Mail newspaper said Johnson said at an October meeting at Downing Street: "No more ****ing lockdowns - let the bodies pile high in their thousands."
Johnson's office has dismissed the damning accusations, insisting all "reportable donations" are transparently disclosed and that the prime minister "has never interfered in a government leak inquiry".
India will be added to England's travel "red list" from Friday, as cases of the UK variant continue to grow.
British Prime Minister Boris Johnson on Monday cancelled a planned trip to India, scheduled to take place next week, due to the current coronavirus situation in India.
"I indeed share the widespread concern about some of the stuff that we're reading at the moment ... and I know that the Cabinet Secretary shares my concern as well," Johnson told parliament, saying top civil servants should have experience of the private sector but it was not clear that "those boundaries have been properly understood".
"The Cabinet Office is commissioning an independent review on behalf of the prime minister to establish the development and use of supply chain finance and associated activities in government and the role Greensill played in those," he told reporters.
This independent review will also look at how contracts were secured and business representatives engaged with government. It will be led by legal expert Nigel Boardman.
Northern Irish justice minister Naomi Long, of the centrist Alliance Party, noted that Johnson and Lewis "denied the existence of borders, even as those borders were being erected".
"It was with great sadness that a short time ago I received word from Buckingham Palace that His Royal Highness the Duke of Edinburgh has passed away at the age of 99.
"Prince Philip earned the affection of generations here in the United Kingdom, across the Commonwealth and around the world.
"I don't think that anything I have seen leads me to suppose that we will have to change the roadmap or deviate from the roadmap in any way," Johnson said.
Under the current plan international travel will not resume until May 17 at the earliest. The Financial Times said Johnson was not expected to set out a specific timeframe.
"I'm afraid you can see what's happening in France... It's very sad actually - it's very very sad," Johnson said. "When they get it in France and they get it bad, two or three weeks later it comes to us.
"I don't want to say that the government is going to agree with absolutely everything in it, but it has some original and stimulating work in it but I think people need to read and to consider," Johnson said.
"There are very serious issues that our society faces to do with racism that we need to address, we've got, we've got to do more to fix it and we need to understand the severity of the problem," he said.