Conventional sources of Galactic cosmic rays are believed to be supernovae and supernova remnants that are powerful enough to accelerate particles up to 10(17) eV. Meanwhile, an interpretation of recent experimental data obtained by PAMELA, Fermi-LAT, and AMS-02 spectrometers hints at a possibility that some cosmic-ray sources may be located in a close proximity of the solar system, at the distances less than 1 kpc. Presence of such local sources could explain the unexpected raise of the positron fraction in cosmic rays, complex shapes of the proton and helium spectra, and even anomalous low-energy cosmic rays. We consider active dwarf stars as possible sources of Galactic cosmic rays in the energy range up to 10(14) eV. These stars are producing powerful stellar flares. Meanwhile, generation of high-energy cosmic rays should be accompanied by the high-energy gamma-ray emission, which may be observed. Here we present the results of the SHALON long-term observations aimed to search for gamma-ray emission above 800 GeV from the active red dwarf stars.