Summary: In a graph \(G\), a geodesic between two vertices \(x\) and \(y\) is a shortest path connecting \(x\) to \(y\). A subset \(S\) of the vertices of \(G\) is in general position if no vertex of \(S\) lies on any geodesic between two other vertices of \(S\). The size of a largest set of vertices in general position is the general position number that we denote by \(\operatorname{gp}(G)\). Recently, M. Ghorbani et al. [Discuss. Math., Graph Theory 41, No. 4, 1199–1213 (2021; Zbl 1468.05057)] proved that for any \(k\) if \(n\geq k^3-k^2+2k-2\), then \(\operatorname{gp}(Kn_n,k)=\binom{n -1}{k-1}\), where \(Kn_{n,k}\) denotes the Kneser graph. We improve on their result and show that the same conclusion holds for \(n\geq 2.5k-0.5\) and this bound is best possible. Our main tools are a result on cross-intersecting families and a slight generalization of Bollobás’s inequality on intersecting set pair systems.