In this paper we prove that given two sets $E_1,E_2 \subset \mathbb{Z}$ ofpositive density, there exists $k \geq 1$ which is bounded by a numberdepending only on the densities of $E_1$ and $E_2$ such that $k\mathbb{Z}\subset (E_1-E_1)\cdot(E_2-E_2)$. As a corollary of the main theorem we deducethat if $\alpha,\beta > 0$ then there exist $N_0$ and $d_0$ which depend onlyon $\alpha$ and $\beta$ such that for every $N \geq N_0$ and $E_1,E_2 \subset\mathbb{Z}_N$ with $|E_1| \geq \alpha N, |E_2| \geq \beta N$ there exists $d\leq d_0$ a divisor of $N$ satisfying $d \, \mathbb{Z}_N \subset(E_1-E_1)\cdot(E_2-E_2)$.
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