NAB chairman Michael Chaney said yesterday the company would continue to pursue a sale of its UK banking arm but there is no buyer yet.
Mr Thorburn, who runs the Bank of New Zealand, is to replace Cameron Clyne as chief executive this summer. It has not yet been decided whether he will take over from Mr Clyne as chairman of Clydesdale.
"I'm sure Andrew will be as diligent as Cameron in looking for opportunities to dispose of that business," Mr Chaney said, according to the Sydney Morning Herald.
His comments indicate NAB is keen for a sale even though Glasgow-based Clydesdale has long insisted the group is open to "all options" for the business.
Mr Chaney said it is too early to plan the use of any proceeds.
"The world changes and capital requirements change from year to year.
"Given [that] it is not going to be sold tomorrow, it would be silly to speculate," he said.
Some NAB investors blame Clydesdale Bank, which also owns Yorkshire Bank, for dragging on performance.
A Clydesdale spokesman said: "Look, there is a lot of speculation. We would not comment on that.
"The board has said for a long time it will look at all options. It won't rush into anything.
"Nothing is off the table but they will do what delivers shareholder value."
Under chief executive David Thorburn, Clydesdale recently returned to profitability after being hit by property loan losses in the recession.