The aim of this study is to set a baseline for the jet quenching measurements of the Quark Gluon Plasma (QGP) formed in the large system size Nucleus-Nucleus (A-A) at top central collisions, via studying simulated small system size, Nucleon-Nucleon (N-N) collisions. The proton-proton (p-p) collisions were simulated using PYTHIA, at center of mass energies √ s N N = 200 GeV and √ s N N = 13 T eV corresponding to the available energies at the current collider experiments; the Relativistic Heavy Ion Collider (RHIC), and the Large Hadron Collider (LHC). At both energies, the two-particle azimuthal correlation functions have been considered, and the yield associated with the high transverse momentum (p T ) particles were extracted at its near-side (∆φ ≈ 0) and away-side (∆φ ≈ π) at mid pseudo rapidity (|η| ≤ 2). The ratio between the near-side yields in the high multiplicity events to these of the low multiplicity events (I N HL ), as well as, the ratio of the away-side yields (I A HL ) were calculated at both energies as a function of the hadron fractional energy z T of the high-p T particle. At both energies, the values of I N HL and I A HL were less than unity, and of trivial dependence on z T . The values of I A HL are always less than these of I N HL at the same multiplicity and energy, and both quantities show a pattern of systematic decreases with the multiplicity. Such multiplicity dependence cannot be used neither to exclude the jet quenching nor to prove it in the high multiplicity events in p-p collisions, as the suppressions have been found at both sides, near and away of the high-p T particle.