The increasing computational load required by most applications and the limits in hardware performances affecting scientific computing contributed in the last decades to the development of parallel software and architectures. In Fluid-Structure Interaction (FSI, in short) for haemodynamic applications, parallelization and scalability are key issues (see~\cite{formaggia09:_cardiov_mathem}). In this work we introduce a class of parallel preconditioners for the FSI problem obtained by exploiting the block-structure of the linear system. We stress the possibility of extending the approach to a general linear system with a block-structure, then we provide a bound in the condition number of the preconditioned system in terms of the conditioning of the preconditioned diagonal blocks, finally we show that the construction and evaluation of the devised preconditioner is modular. The preconditioners are tested on a benchmark 3D geometry discretized in both a coarse and a fine mesh, as well as on two physiological aorta geometries. The simulations that we have performed show an advantage in using the block preconditioners introduced and confirm our theoretical results.