Recently, the gradient flow has attracted a considerable amount of attention in the lattice QCD community. The hope is that this technique will enable us to determine a host of important observables with unprecedented precision. The running coupling is an important example, the knowledge of which with a high accuracy is most desirable since its error enters in many other quantities. Its perturbative expansion is an important ingredient for a precise determination.
However, the diagrammatic approach is particularly cumbersome when employing the gradient flow, which makes numerical stochastic perturbation theory a promising candidate for a method to perform the required calculations. We will report on the status of an ongoing effort to compute the gradient flow coupling in NSPT.