While task-based programming, such as OpenMP, is a promising solution to exploit large HPC compute nodes, it has to be mixed with data communications like MPI. However, performance or even more thread progression may depend on the underlying runtime implementations. In this paper, we focus on enhancing the application performance when an OpenMP task blocks inside MPI communications. This technique requires no additional effort on the application developers. It relies on an online task reordering strategy that aims at running first tasks that are sending data to other processes. We evaluate our approach on a Cholesky factorization and show that we gain around 19% of execution time on an Intel Skylake compute nodes machine-each node having two 24-core processors.