Councillors in Greater Manchester said they would investigate loans made to companies linked to Sheikh Mansour bin Zayed al-Nahyan as part of a fund operated by the combined authority when Mr Burnham led it.
In 2017, three companies ultimately controlled by Sheikh Mansour, the UAE's vice-president and deputy prime minister, were loaned £55m to help finance Manchester Life, a housing development that promised 6,000 homes. The Greater Manchester Combined Authority said the loans had been repaid in full, but has not disclosed the interest rate or why Sheikh Mansour's companies were eligible for public money.
John Leech, the Liberal Democrat councillor who chairs the GMCA's overview and scrutiny committee, told the BBC the approval process had been criticised as "very opaque in the past". He said it was "not unreasonable" to ask why successful businesses needed to borrow public money. "In the case of Abu Dhabi, you would imagine that they wouldn't have any problem accessing funds from elsewhere as well," he said.
The fund has handed out £1bn to 50 developers since 2015. Mr Leech said the process "does seem to be out of kilter with what the original stated aims were back in 2015".
The investigation follows the emergence last week of a meeting between Mr Burnham and City's owners at the Etihad Stadium, weeks before the loans were approved. The meeting had disappeared from public records, prompting Mr Burnham to ask the GMCA to carry out a "manual trawl" of his meetings to ensure "full transparency".
Mr Burnham, who earlier said the owners had been "such a huge partner in the building of modern Manchester" and that he would be "really concerned" to lose them from the sport, faced accusations he sided with the club after its financial breach.
A GMCA spokesperson said the authority was supporting the committee's inquiries. The fund had built 11,000 new homes and contributed "billions of pounds worth of development at no cost to the taxpayer", they said, adding that decisions on loans were taken publicly and lending criteria reflected "due diligence standards in the private sector". Downing Street declined to comment.