The $632m container terminal in Kaohsiung is being jointly developed by Yang Ming Marine and the Taiwan government.
According to a Dow Jones report, if the talks turn succesful the aqcuision will be carried out by COSCO's port investment arm, Cosco Pacific Ltd and Yang Ming Marine.
If the deal gets the go-ahead from the Taiwan government, COSCO will be the first Chinese mainland company to invest in a Taiwanese port.