  In this paper the notion of Ricci $\rho$-soliton as a generalization of Ricci
soliton is defined. We are motivated by the Ricci-Bourguignon flow to define
this concept. We show that if a 3- dimensional almost Kenmotsu Einstein
manifold $M$ be a $\rho$-soliton, then $M$ is a Kenmotsu manifold of constant
sectional curvature $-1$ and the $\rho$-soliton is expanding, with $\lambda
=2$.
