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

Weak $K\to \pi$ generalized form factors and transverse transition quark-spin density from the instanton vacuum