The bank "was planning to announce the executive changes shortly," the paper wrote, citing unnamed sources familiar with the firm.
The UBS chairman, Marcel Ospel, 57, will stay on in his post for another three years, the paper reported.
Wuffli, 49, has presided over a difficult period for the bank marked by the costly closure of an in-house hedge fund, Dillon Read Capital Management (DRCM), which faltered badly in the mortage market.
Wuffli's expected successor, deputy CEO Marcel Rohner, 42, comes from the private-banking and wealth-management side of the business, the paper said.