Constructing "maximal" quotient that is a local system on $\mathbb{C}^×$

Question

Consider $\mathbb{C}^×$ with its analytic topology and a sheaf $M$ of $\mathbb{C}$-vector spaces on it. I want to find a way to find a subsheaf $N\subset M$ such that

1. $N$ has no subsheaves that are local systems,
2. $M/N$ is a local system.

Is there a way to do this? This should help in comparing the derived categories with constructible cohomology and the derived category of constructible sheaves on $\mathbb{C}$.