We study the pion and kaon properties in nuclear medium at nonvanishing temperature and baryon density as well as in the presence of magnetic field in the Nambu--Jona-Lasinio (NJL) model with the help of the proper-time regularization scheme, simulating a confinement. The density dependent of the quark masses are obtained from the quark-meson coupling (QMC) model in the symmetric nuclear matter at the quark level. We analyze the quark condensate, dynamical mass, pion and kaon masses, pion- and kaon-quark coupling constants as well as wave function renormalization factors for those mesons of finite temperature and in the presence of magnetic field for different baryon densities. We find the chiral condensate for the up quark suppresses with increasing temperature and baryon density and enhances under the presence of magnetic field. Interestingly, we find that the wave function renormalization for the pion and kaon increases with respect to the temperature and decreases as the baryon density increases.
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