We discuss the dependence of J/ψ production on the charged particle multiplicity in proton-proton collisions at LHC energies. We show that, in the framework of parton saturation or string interaction models, the hard J/ψ production exhibits a significant growth with the multiplicity, which is stronger than linear in the high density domain. This departure from linearity, that should affect any hard observable, applies for high multiplicity proton-proton collisions in the central rapidity region and is a consequence of the parton saturation or the strong interaction among colour ropes that take place at LHC energies. Our assumption, the existence of coherence effects present in proton-proton collisions at high energy, can also be checked by studying the particular shape of the probability distribution associated to the J/ψ production.RHIC [1,2,3,4] and LHC [5,6,7] data on heavy-ion collisions have shown several important features which indicate the formation of a high density partonic medium with characteristic properties as the low shear viscosity and high opacity. Since the energy density achieved in high multiplicity events produced in pp collisions at LHC is comparable to the reached density in CuCu central collisions or AuAu peripheral collisions at √ s N N = 200 GeV, it is pertinent to wonder about the possibility to obtain a similar high density medium which would be reflected in experimental observables, similar to heavy-ion collisions. An illustration of this would be the predicted ridge structure [8,9] observed by CMS collaboration [10] in pp collisions. Also, the eventuality that other observables, as long range rapidity correlations [11,12,13], energy loss [14], or the elliptic flow [15,16], are measurable in pp collisions, has been reckoned with in different frameworks.We address here to the J/ψ production in high multiplicity pp collisions. We will show that the rise of J/ψ production in the highest multiplicity events observed by the ALICE collaboration [17] can be naturally explained as a consequence of string interaction or parton saturation. This feature is particularly important, since, due to the absence of nuclear effects in this case, it can be use as a baseline in order to disentangle different mechanism that are expected in heavy-ion collisions, as the J/ψ suppression due to sequential dissociation [18] or the J/ψ enhancement due to the recombination of uncorrelated c andc quarks [19].