Speaking in an interview with Fox News broadcast on Sunday, Mr Trump said: "I don't know why we have to be bound by a One China policy unless we make a deal with China having to do with other things, including trade."
Mr Trump also said China was not co-operating with the US on its handling of its currency, on North Korea, or on tensions in the South China Sea.
US policy since 1979 has respected China's stance on Taiwan, which it sees as a breakaway province.
Relations with China became strained when Mr Trump took a phone call from Taiwanese President Tsai Ing-wen.
(Excerpts from BBC)