The multiplicity dependence of heavy flavour production in pp-collisions at LHC energies is studied in the framework of the multi-pomeron exchange model. The model is introducing the string-string interaction collectivity effects in pp collisions, which modifies multiplicity and transverse momenta, leading to the non-trivial mean p_t vs. multiplicity (< p_t> N_ch - N_ch). correlation. The string collectivity strength parameter is fixed by experimental data on multiplicity and transverse momentum correlation in a wide energy range (from ISR to LHC). The particles discrimination is implemented according to Schwinger mechanism taking into account the strong decays of hadron resonances. We demonstrate, that the faster-than-linear growth of the open charm production with the event charged particle multiplicity, observed in experimental pp high energy collisions, can be explained by the modification of the string tension due to the increasing overlap and interaction of quark-gluon strings. The model is extended for p-A interactions and the calculations for p-Pb collisions are performed.