An activist investor pushing for a breakup of UBS will meet with a top executive of the Swiss bank next week, according to a person familiar with the situation, providing a chance to pitch the financial giant on the idea of shedding its investment bank.

The meeting between representatives of Knight Vinke Asset Management and Tom Naratil, the bank's chief financial officer, will come roughly a month after the New York-based investor group argued in an open letter that separating the investment bank from UBS's core wealth-management and retail-banking operations would make the bank less risky and unlock value for shareholders.