Realizing single photon sources emitting in the telecom band on silicon substrates is essential to reach complementary-metal-oxide-semiconductor (CMOS) compatible devices that secure communications over long distances. In this work, we propose the monolithic growth of needlelike tapered InAs/InP quantum dot-nanowires (QD-NWs) on silicon substrates with a small taper angle and a nanowire diameter tailored to support a single mode waveguide. Such a NW geometry is obtained by a controlled balance over axial and radial growths during the gold-catalyzed growth of the NWs by molecular beam epitaxy. This allows us to investigate the impact of the taper angle on the emission properties of a single InAs/InP QD-NW. At room temperature, a Gaussian far-field emission profile in the telecom O-band with a beam divergence angle θ = 30° is demonstrated using a single InAs QD embedded in a 2° tapered InP NW. Moreover, single photon emission is observed at cryogenic temperature for an off-resonant excitation and the best result, g2(0) = 0.05, is obtained for a 7° tapered NW. This all-encompassing study paves the way for the monolithic growth on silicon of an efficient single photon source in the telecom band based on InAs/InP QD-NWs.