We consider Brans-Dicke (BD) scalar tensor theory in the conformally transformed Einstein frame. In this frame BD theory behaves like an interacting quintessence model. We find the necessary conditions on the form of the potential $V(\\\\\\\\varphi)$ in order to have thawing behavior. Finally, by setting the BD coupling constant $\\\\\\\\omega=0$, the metric $f(R)$ gravity has been considered in the Einstein frame. Assuming the existence of thawing solution, some necessary conditions for $f(R)$ gravity models have been derived.

Keywords