BRUSSELS—The European Union could drop controversial investor-protection rules from its free-trade talks with the U.S., but the bloc is unlikely to do the same for its trade deal with Canada, its designated trade commissioner said.

At a confirmation hearing in the European Parliament, Cecilia Malmström of Sweden said she couldn't rule out removing the investor-state dispute settlement clause from the proposed Transatlantic Trade and Investment Partnership with the U.S. The clause would allow investors to apply directly to...