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 √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, v₂*, is observed to decrease with N_ch^j. This trend is well described by Monte Carlo event generators. However, a rising trend for v₂* 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.