Narrowing a microstrip's tip
Is it possible the narrow down the width around that area while maintaining the 50 ohm impedance of the microstrip?


Narrowing the trace will increase its inductance (per unit length), which will increase the characteristic impedance \$Z_0\$. But you could cut out the ground plane beneath the chip's pad and a few 100 um of trace to reduce the capacitance to compensate. Doing this correctly might require optimizing the design using a 3D EM solver tool.

More realistically, though, consider that the wavelength corresponding to 1.6 GHz is somewhere between 90 and 190 mm, depending on the transmission line geometry (and the substrate Dk). A short mismatched stub of 4 or 5 mm at the end of your track is not likely to noticeably impact the return loss seen looking into the chip, so it's reasonable to just narrow the trace for a short distance and then connect it to the matched trace.