But the share price dived after a Santander spokesman denied the report.
NAB shares fell 20 cents, or 0.74 per cent, shortly after the Australian market opened on Tuesday but, at 1118 AEDT, had recovered to be 10 cents, or 0.37 per cent, down at $26.75.
In April, NAB said it would cut 1,400 jobs as it restructured its UK business.
He said the market widely considered NAB's UK banks to be a drain on its results and any news that it may be able to sell them would prompt a share price surge.
"Some analysts think it will unlock around $2 billion worth of value for NAB," he said.
"It's been an underperforming asset for some time and it's really held back a lot of investors from investing in NAB.
"So, I think it's widely considered a positive if they can unload these UK assets and move on."
"The market would like to see them get rid of those UK assets. Other than that, it will focus on local factors and see how they perform here as opposed to their peers," he said.
"But those UK assets will continue to be the elephant in the room for NAB."