  Both coherence and entanglement stem from the superposition principle,
capture quantumness of a physical system, and play a central role in quantum
physics. In a multipartite quantum system, coherence and quantum correlations
are closely connected. In particular, it has been established that quantum
coherence of a bipartite state is an important resource for its conversion to
entanglement [A. Streltsov {\it et al.}, Phys. Rev. Lett. {\bf 115}, 020403
(2015)] and to quantum discord [J. Ma {\it et al}., Phys. Rev. Lett. {\bf 116},
160407 (2016)]. We show here that there is a very close association between
partial coherence introduced by Luo and Sun [S. Luo and Y. Sun, Phys. Rev. A
{\bf 96}, 022136 (2017)] and quantum correlations (quantified by quantum
discord) in both directions. Furthermore, we propose families of coherence
measures in terms of quantum correlations and quantum Fisher information.
