The spatial distribution of the forward-propagating amplified spontaneous emission (ASE) of nitrogen molecular ions during femtosecond laser filamentation in air is studied via numerical simulations. The results suggest that the divergence angle and signal intensity are extremely sensitive to the external focal length. Concurrently, we show that the optical Kerr effect plays a significant role in concentrating the directivity of ASE signals, particularly in cases of loose focusing. Furthermore, the simulations demonstrate that ASE signals are enhanced for a tight focus, although the corresponding filament length is shorter. The main physical mechanism underlying this process is the competition between the plasma defocusing and optical Kerr effects. The result is important for filamentation-based light detection and ranging applied to remote sensing.