  We show that a suitable notion of Dirac-Jacobi structure on a generic line
bundle $L$, is provided by Dirac structures in the omni-Lie algebroid of $L$.
Dirac-Jacobi structures on line bundles generalize Wade's $\mathcal E^1
(M)$-Dirac structures and unify generic (i.e.~non-necessarily coorientable)
precontact distributions, Dirac structures and local Lie algebras with one
dimensional fibers in the sense of Kirillov (in particular, Jacobi structures
in the sense of Lichnerowicz). We study the main properties of Dirac-Jacobi
structures and prove that integrable Dirac-Jacobi structures on line-bundles
integrate to (non-necessarily coorientable) precontact groupoids. This puts in
a conceptual framework several results already available in literature for
$\mathcal E^1 (M)$-Dirac structures.
