  There is growing interest in the development of a muon collider that would
make it possible to produce lepton collisions at energies of several TeV. Among
others, there can be significant contributions to electroweak gauge boson,
Higgs boson and top quark physics. In this work we pay attention to the latter,
in particular, effective flavor-changing top-quark interactions. We discuss two
flavor changing $t \bar q$ ($q=u,c$) production processes that can be a good
probe of the dimension-six top quark and gauge boson operators in the SMEFT. We
consider all nine operators that can generate flavor-changing top quak
couplings. After comparing with the current LHC limits, we identify two of them
that have the highest sensitivity. On the other hand, for two others the
sensitivity is so low that they can be safely discarded from future studies.
