Hi,

Here is a theorem that might answer your question (it is coming from Chesnay, Jeanblanc-Piqué and Yor's book  "Mathematical Methods for Financial Markets"). 

It is theorem (11.2.8.1 page 621) here it is :

Let $X$ be an $R^d$ valued Lévy Process and $F^X$ its natural filtration. Let $M$ be an $F^X$-local Martingale. Then there exist an $R^d$-valued predictable process $\phi$ and an predictable function $\psi : R^+ \times \Omega \times R^d\to R$ such that :

-$\int_0^t \phi^i(s)^2ds <\infty$ almost surely   

-$\int_0^t \int_{|x|\le 1} |\psi(s,x)|ds\nu(dx) <\infty$ almost surely   

-$\int_0^t \int_{|x|> 1} \psi(s,x)^2ds\nu(dx) <\infty$ almost surely   


and  

$M_t=M_0+  \sum_{i=0}^d \int_0^t \phi^i(s)dW^i_s + \int_0^t \int_{R^d} \psi(s,x)\tilde{N}(ds,dx)$

Where $\tilde{N}(ds,dx)$ is the compensated measure of the Lévy process $X$ and $\nu$ the associated Lévy measure.

Moreover if $(M_t)$ is square integrable martingale then we have :

$E[(\int_0^t \phi^i(s)dW^i_s)^2]=E[\int_0^t \phi^i(s)^2ds]<\infty$

and 

$E[(\int_0^t \int_{R^d} \psi(s,x)\tilde{N}(ds,dx))^2]=E[ \int_0^t ds \int_{R^d} \psi(s,x)^2\nu(dx)]<\infty$

and $\phi$ and $\psi$ are essentially unique. 

The theorem is not proved in the book but there is a reference to the following parpers :

1/H. Kunita and S. Watanabe. On square integrable martingales. Nagoya J.
Math., 30:209–245, 1967

2/H. Kunita. Representation of martingales with jumps and applications to
mathematical finance. In H. Kunita, S. Watanabe, and Y. Takahashi, editors,
Stochastic Analysis and Related Topics in Kyoto. In honour of Kiyosi Itô,
Advanced studies in Pure mathematics, pages 209–233. Oxford University
Press, 2004.

Regards