Violation of Leggett-Garga's inequalities means that the system shows a type of non-classical correlation that exhibited by quantum observables measured at different moments of times. These correlations are used, for example, to test macroscopic realism, assess the "quantumness" of the system, and in the protocols in information theory. Despite well-established results regarding correlation in time for closed systems, the area of open systems is still poorly explored. The main purpose of the presented research is to determine the impact of interaction with the external environment on the resource of non-classical correlations of the actual measured subsystem. We present various physical models of open systems, i.e. weak coupling with the thermal environment, perturbation caused by white noise, and spin-spin coupling. The obtained results demonstrate that the environment may have a non-trivial effect on the correlations in the subsystem.