  In this work we study the cosmological attractor models of inflation in
connection with certain scalar-tensor theories of gravity, e.g $f(R)$ gravity
and Brans-Dicke theory. For some particular choices of the functional degrees
of freedom in these theories, one obtains Starobinsky like predictions in the
($n_s$-$r$) observable plane. We have demonstrated that these choices in the
Lagrangian density of certain $f(R)$ and Brans-Dicke theories fulfil the
condition of the cosmological attractors. That explains why known predictions
of $f(R)$ and Brans-Dicke theories in certain cases appear to be the
predictions of the much discussed attractor theories. In addition, we did an
analysis showing how the predictions of an attractor model is preserved with
respect to the variation in the functional freedom of the theory.
