Qatar has expressed an interest in investing in the part-nationalised Royal Bank of Scotland and Lloyds Banking Group.
"About any investment in the state or partially-state owned banks, we are very open for any investment in the UK," Prime Minister Sheikh Hamad bin Jassim said.
The UK government plans to sell its 83% stake in RBS and 43% holding in Lloyds.
Qatar invested heavily in Barclays in the wake of the financial crisis.
And last year the Qatari royal family's investment company bought Harrod's for a reported £1.5bn, while the Qatar Investment Authority owns about a quarter of retailer Sainsbury's.
After meeting UK Prime Minister David Cameron, the Qatari prime minister expressed interest in doing more deals with UK companies.
Sheikh Hamad bin Jassim said he had "discussed some ideas" with Mr Cameron, who was visiting Qatar on Wednesday as part of a Middle East tour.
"Our team has been engaged and we will continue to discuss investment in the UK," he added.
The government's stakes in the part-nationalised banks, which also include Northern Rock and Bradford & Bingley are managed by UKFI.
UKFI declined to comment on the suggestion of interest from Qatar.
However it has previously said that no sale was likely until RBS and Lloyds had seen some share price stability and until the government's Independent Commission on Banking (ICB) was published.
Last month, the head of UKFI warned that if the ICB recommended a break-up of British banks, this would damage taxpayers' returns from their stakes - worth about £67bn at the time of investment.