In the last few decades, graphics processing units (GPUs) have been used to efficiently solve linear systems by means of preconditioned Krylov subspace methods. The preconditioner is required to have a high degree of parallelism to exploit the potential of GPUs for massive data processing. An approximate inverse (AINV) preconditioner is suitable for GPU implementation because its preconditioning operations mainly consist of sparse matrix-vector multiplication. However, an AINV algorithm, the algorithm to construct the AINV preconditioner, usually requires more time than construction algorithms for other preconditioners, such as the ILU/IC factorization. Therefore, it is necessary to improve the AINV algorithm to make AINV preconditioning more attractive. In this study, we propose a new version of the AINV algorithm: the SD-AINV algorithm, by introducing a statically defined approximation based on nonzero element positions of a coefficient matrix. The SD-AINV algorithm is expected to run faster than the AINV algorithm because the approximation reduces the computational cost of the AINV algorithm. In addition, the approximation enables parallel implementations of the SD-AINV algorithm using nodal/block multi-color ordering. Numerical experiments show that the SD-AINV algorithm constructs the preconditioner faster than the conventional AINV algorithm without significantly degrading the performance of the preconditioned conjugate gradient method.