  We associate with every Renner monoid $R$ a \emph{generic Hecke algebra}
$\H(R)$ over $\mathbb{Z}[q]$ which is a deformation of the monoid
$\mathbb{Z}$-algebra of $R$. If $M$ is a finite reductive monoid with Borel
subgroup $B$ and associated Renner monoid $R$, then we obtain the associated
Iwahori-Hecke algebra $\H(M,B)$ by specialising $q$ in $\H(R)$ and tensoring by
$\mathbb{C}$ over $\mathbb{Z}$, as in the classical case of finite algebraic
groups. This answers positively to a long-standing question of L. Solomon.
