A wireless device (400), a higher layer node (404) and methods therein, for handling measurement reporting in a wireless network as performed by the wireless device (400). The wireless device (400) detects (4:1) a coverage object being a cell or a beam not contained in a predefined first list of coverage objects for which the wireless device (400) is required to send measurement reports to a lower layer node (402) operable according to at least one of layer 1 and layer 2. The wireless device (400) then measures a radio signal of the coverage object where the measured radio signal fulfils a predefined event condition, and sends (4:2B) a measurement report of said measuring to a higher layer node (404) operable according to one or more layers above layer 1 and layer 2.