  We study the classical Euclidean wormholes in the context of extended
theories of gravity. With no loss of generality, we use the dynamical
equivalence between $f(\tilde{R})$ gravity and scalar-tensor theories to
construct a point-like Lagrangian in the flat FRW space time. We first show the
dynamical equivalence between Palatini $f(\tilde{R})$ gravity and the
Brans-Dicke theory with self-interacting potential, and then show the dynamical
equivalence between the Brans-Dicke theory with self-interacting potential and
the minimally coupled O'Hanlon theory. We show the existence of new Euclidean
wormhole solutions for this O'Hanlon theory and, for an special case, find out
the corresponding form of $f(\tilde{R})$ having wormhole solution. For small
values of the Ricci scalar, this $f(\tilde{R})$ is in agreement with the
wormhole solution obtained for higher order gravity theory $\tilde{R}+\epsilon
\tilde{R}^2,\epsilon<0$.
