In this talk, I will introduce the notion of a Nijenhuis-Lie bialgebra as a Nijenhuis endomorphism $n: {\frak g} \to {\frak g}$ on a Lie algebra ${\frak g}$ which is compatible, in a suitable sense, with a Lie bialgebra structure on ${\frak g}$. An interesting example (the Euler top) that motivates the previous definition and some results on the algebraic structure of a Nijenhuis-Lie bialgebra will be presented. I will also consider the Nijenhuis-Lie bialgebra in the case that Lie bialgebras are coboundary which turns to the $r$-$n$ structures. The Nijenhuis-Lie bialgebra structures are a starting point to get a deeper insight into the underlying geometric structures of the bi-Hamiltonian systems on Poisson-Lie groups.