This paper is concerned with some properties of the generalized Ornstein–Uhlenbeck operator $$\begin{aligned} -A_{\Phi ,G}+\nu V:=-\Delta +\nabla \Phi \cdot \nabla -G\cdot \nabla +\nu V, \end{aligned}$$ with nonnegative singular potential $$\nu V(x)$$ in the weighted space $$L^{p}({\mathbb {R}}^{N},\mu )$$ , $$1<p<\infty $$ , where $$\mu (dx)=e^{-\Phi (x)}dx$$ . Sufficient conditions ensuring the m-accretivity, m-sectoriality and m-dispersivity of $$-A_{\Phi ,G}+\nu V$$ in $$L^{p}({\mathbb {R}}^{N},\mu )$$ are presented. Particularly, it is shown that $$A_{\Phi ,G}-\nu V$$ with a suitable domain is the generator of a quasi-contractive and positivity preserving analytic $$C_0$$ -semigroup in $$L^{p}({\mathbb {R}}^{N},\mu )$$ . Further, generation of quasi-contractive analytic semigroups by $$A_{\Phi ,G}-(\nu +k)V$$ in $$L^{p}({\mathbb {R}}^{N},\mu )$$ , for some $$\nu >0$$ and $$ k\in {\mathbb {C}}$$ , is proven. The results improve and complete the recent results established in Metafune et al. (Adv Differ Equ 10(10):1131–1164, 2005) when $$V\equiv 0$$ and Kojima and Yokota (J Math Anal Appl 364(2):618–629, 2010) and Sobajima and Yokota (J Math Anal Appl 403(2):606–618, 2013) when $$0\le V\in C^1({\mathbb {R}}^N)$$ . Some examples where our results can be applied are provided, including Kolmogorov operators and operators with polynomially growing drift term.