The noncentrosymmetric transition-metal monopnictides NbP, TaP, NbAs, and TaAs are a family of Weyl semimetals in which pairs of protected linear crossings of spin-resolved bands occur. These so-called Weyl nodes are characterized by integer topological charges of opposite sign associated with singular points of Berry curvature in momentum space. In such a system, anomalous magnetoelectric responses are predicted, which should only occur if the crossing points are close to the Fermi level and enclosed by Fermi surface pockets penetrated by an integer flux of Berry curvature, dubbed Weyl pockets. TaAs is shown to possess Weyl pockets, whereas TaP and NbP have trivial pockets enclosing zero net flux of Berry curvature. Herein, via measurements of the magnetic torque, resistivity, and magnetization, a comprehensive quantum-oscillation study of NbAs is presented, the last member of this family where the precise shape and nature of the Fermi surface pockets is still unknown. Seven distinct frequency branches, three of which have not been observed before, are detected. A comparison with density functional theory calculations suggests that the two largest pockets are topologically trivial, whereas the low frequencies might stem from tiny Weyl pockets. The enclosed Weyl nodes are within a few meV of the Fermi energy.