We show that the moduli spaces of stable sheaves on projective schemes admit
certain non-commutative structures, which we call quasi NC structures,
generalizing Kapranov's NC structures. The completion of our quasi NC structure
at a closed point of the moduli space gives a pro-representable hull of the
non-commutative deformation functor of the corresponding sheaf developed by
Laudal, Eriksen, Segal and Efimov-Lunts-Orlov. We also show that the framed
stable moduli spaces of sheaves have canonical NC structures.Comment: 42 page