  We investigate the inflationary attractors in models of inflation inspired
from general conformal transformation of general scalar-tensor theories to the
Einstein frame. The coefficient of the conformal transformation in our study
depends on both the scalar field and its kinetic term. Therefore the relevant
scalar-tensor theories display the subset of the class I of the degenerate
higher-order scalar-tensor theories in which both the scalar field and its
kinetic term can non-minimally couple to gravity. We find that if the conformal
coefficient $\Omega$ takes a multiplicative form such that $\Omega \equiv
w(\phi)W(X)$ where $X$ is the kinetic term of the field $\phi$, the theoretical
predictions of the proposed model can have usual universal attractor
independent of any functions of $W(X)$. For the case where $\Omega$ takes an
additive form, such that $\Omega \equiv w(\phi) + k(\phi) \Xi(X)$, we find that
there are new $\xi$ attractors in addition to the universal ones. We analyze
the inflationary observables of these models and compare them to the latest
constraints from the Planck collaboration. We find that the observable
quantities associated to these new $\xi$ attractors do not satisfy the
constraints from Planck data at a strong coupling limit.
