A search for collective effects inside jets produced in proton-proton collisions is performed via correlation measurements of charged particles using the CMS detector at the CERN LHC. The analysis uses data collected at a center-of-mass energy of sqrt[s]=13 TeV, corresponding to an integrated luminosity of 138 fb^{-1}. Jets are reconstructed with the anti-k_{T} algorithm with a distance parameter of 0.8 and are required to have transverse momentum greater than 550 GeV and pseudorapidity |η^{jet}|<1.6. Two-particle correlations among the charged particles within the jets are studied as functions of the particles' azimuthal angle and pseudorapidity separations (Δϕ^{*} and Δη^{*}) in a jet coordinate basis, where particles' η^{*}, ϕ^{*} are defined relative to the direction of the jet. The correlation functions are studied in classes of in-jet charged-particle multiplicity up to N_{ch}^{j}≈100. Fourier harmonics are extracted from long-range azimuthal correlation functions to characterize azimuthal anisotropy for |Δη^{*}|>2. For low-N_{ch}^{j} jets, the long-range elliptic anisotropic harmonic, v_{2}^{*}, is observed to decrease with N_{ch}^{j}. This trend is well described by Monte Carlo event generators. However, a rising trend for v_{2}^{*} emerges at N_{ch}^{j}≳80, hinting at a possible onset of collective behavior, which is not reproduced by the models tested. This observation yields new insights into the dynamics of jet evolution in the vacuum.