In this paper, a hypothesis that the cosmological gravitational potential can be measured with the use of high- precision atomic clocks is proposed and substantiated. The consideration is made with the use of a quasi-classical description of the gravitational shift that lies in the frame of nonmetric theories of gravity. It is assumed that the cosmological potential is formed by all matter of the Universe (including dark matter and dark energy) and that it is spatially uniform on planet scales. It is obvious that the cosmological potential, Φ
, is several orders of magnitude greater than Earth's gravitational potential φ
on Earth's surface). In our method, the tick rates of identical atomic clocks are compared at two points with different gravitational potentials, i.e. at different heights. In this case, the information on Φ
is contained in the cosmological correction α?0 in the relationship Δω/ω=(1+α)Δφ/c
between the relative change of the frequencies Δω/ω (in atomic clocks) and the difference of the gravitational potential Δφ at the measurement points. We have estimated the low limit of cosmological correction, α>10
. It is shown that using a modern atomic clock of the optical range it is possible to measure the value of α in earth-based experiments if |α|>10
. The obtained results, in the case of their experimental confirmation, will open up new unique opportunities for the study of the Universe and the testing of various cosmological models. These results will also increase the measurement accuracy in relativistic geodesy, chronometric gravimetry, global navigation systems, and global networks of atomic clocks.