Mr Dutton, who has been overseas on leave for three weeks, has been under fire over his role as home affairs minister under the former coalition government.
Nine newspapers reported last week on documents tabled in parliament which showed the Australian Federal Police told Mr Dutton in July 2018 that Sydney-based Mozammil Bhojani was under investigation over suspected bribes to Nauruan politicians.
The payments were made to secure preferential access to millions of dollars worth of phosphate for Mr Bhojani's company Radiance International.
Despite the advice, the Department of Home Affairs entered into a fresh $9.3 million contract with Radiance to provide accommodation for refugees and asylum seekers.
A month after the contract was signed, police arrested Mr Bhojani and charged him with paying bribes to two Nauruan officials.
He pleaded guilty and was convicted in 2020.
Mr Dutton said he was happy to co-sign, with the prime minister, a letter of referral to the National Anti-Corruption Commission.
"If there are allegations, then refer them to the NACC," Mr Dutton told reporters in Canberra on Monday.
"But refer them back to the period of 2012 when the procurement arrangements were put in place (and Labor was in government)."
Mr Dutton said he had checked his records for a briefing he allegedly received but could not find anything.
"As minister I had no involvement whatsoever in relation to the contract negotiations, the execution of the agreements, and that's true for all the predecessors," he said.
"I have nothing to hide."
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