  We derive the forward photoproduction amplitude for the diffractive $\gamma p
\to l^+ l^- p$ reaction in the momentum space. within the formalism of
$k_\perp$- factorization. Predictions for the $\gamma p \to l^+ l^- p$ reaction
are given using unintegrated gluon distribution from the literature. We
calculate the total cross section as a function of photon-proton center of mass
energy and the invariant mass distribution of the lepton pair. We also discuss
whether the production of timelike virtual photons can be approximated by
continuing to the spacelike domain $ q^2 < 0$. The present calculation provides
an input for future predictions for exclusive hadroproduction in the $p p \to p
l^+ l^- p$ reaction.
