Current in the long wire is directed upward .
Given the wire is prependicular to the plane of coil and passing through the center.
The magnetic flux through the coil due to the magnetic field produced by the wire is zero because the magnetic field due to wire is always parallel to the coil and hence there will be no magnetic flux linked with coil.
No matter the coil moves down , up or stay at the same position there will be no magnetic flux linked with the coil.
Thus there will no change in the magnetic flux .
Hence there will be no induced current through the loop.