UBS AG is aiming to eliminate as many as 15 lines of business and a third or more of the jobs at its investment-banking division as part of a plan to restore the business to health, according to people involved with the effort.

UBS's board will meet Monday to weigh the plan, which would lop roughly 10,000 employees from the Swiss bank's total headcount over the next three to five years, the people said. The bulk of the cuts would come at UBS's investment bank, which had 16,432 employees at the end of June.

The...