Given a complex-valued bisequence $s = (s_{ab})_{(a,b) \in \mathbb{N}_0^2 }$ and a closed set $K \subseteq \mathbb{C}$, the complex version of Haviland's theorem, in particular, asserts that there exists a measure $\mu$ with ${\rm supp} \, \mu \subseteq K$ and $$s_{ab} = \int_{\mathbb{C}} z^a \bar{z}^b \, d\mu(z) \quad \quad {\rm for} \quad (a,b) \in \mathbb{N}_0^2$$ if and only if $$p|_K \geq 0 \Longrightarrow L_s(p) \geq 0,$$ where $L_s: \mathbb{C}[z, \bar{z}] \to \mathbb{C}$ is the {\it Riesz-Haviland functional}, i.e., $$L_s(p) = \sum p_{ab} \, s_{ab} \quad \quad {\rm for} \quad p(z,\bar{z}) = \sum p_{a,b} z^a \bar{z}^b.$$ In this talk, we shall consider a quaternionic analogue of the above result, where the complex-valued bisequence $s$ is replaced by a quaternionic bisequence and the integral representation above is replaced by something more complicated involving several measures.