We apply Donaldson-Auroux's asymptotically holomorphic methods to construct asymptotically holomorphic embeddings of presymplectic closed manifolds of constant rank with integral form into Grassmannians ${\rm Gr}(r,N)$ . In particular, we obtain asymptotically holomorphic embeddings into the projective spaces $\bm{C}{\rm P}^{N-1}$ such that the pull-back of the Fubini-Study form is cohomologous to ${k\omega}/{2\pi}$ for large integers $k$ . Moreover, we can construct asymptotically holomorphic immersions along the symplectic distribution of presymplectic manifolds into the projective spaces.