  We investigate the generalized $K\to \pi$ transition vector and tensor form
factors, from which we derive the transverse quark spin density in the course
of the $K\to\pi$ transition, based on the nonlocal chiral quark model from the
instanton vacuum. The results of the transition tensor form factor are in good
agreement with recent data of lattice QCD. The behavior of the transverse quark
spin density of the $K\to\pi$ transition turn out to be very similar to those
of the pion and the kaon.
