The board of Citigroup is growing increasingly dissatisfied with the financial giant's performance, and some directors are considering replacing Sir Win Bischoff as chairman, according to people familiar with the matter.

One leading candidate is Richard Parsons, Time Warner's chairman and a member of Citigroup's board. Parsons ran a New York thrift in the early 1990s and is one of the few Citigroup directors with experience in financial services. He also is part of President-elect Barack Obama's transition economic-advisory board.