I found a solution. It needs to be manually edited to fit to the lenght of the quote and needs to be changed for left/right column, but it works.

\documentclass[a4paper,oneside]{article}
\usepackage[ascii]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
\usepackage[left=3cm,bottom=2cm]{geometry}
\usepackage{amssymb,amsfonts,textcomp}
\usepackage{multicol}
\setlength{\columnsep}{1cm}
\widowpenalty10000
\clubpenalty10000
\usepackage{wrapfig}
\usepackage{lipsum}
\begin{document}
\begin{multicols}{2}
\lipsum[1]
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Proin ac tempus dui. Etiam non mattis neque. Maecenas tempor,
massa a luctus
\begin{wrapfigure}[11]{l}[50pt]{.3\textwidth}
\hspace{20pt}
\begin{minipage}{140pt}
\Large{``Lorem ipsum dolor sit amet, consectetur adipiscing elit luctus sollicitudin, elit massa auctor velit, eu mattis
lacus arcu nec est.''}
\end{minipage}
\end{wrapfigure}
\lipsum[2]
\begin{wrapfigure}[11]{r}[50pt]{.3\textwidth}
\hspace{-20pt}
\begin{minipage}{140pt}
\Large{``Lorem ipsum dolor sit amet, consectetur adipiscing elit luctus sollicitudin, elit massa auctor velit, eu mattis
lacus arcu nec est.''}
\end{minipage}
\end{wrapfigure}
\lipsum[2]
\lipsum[2]
\end{multicols}
\end{document}
It severly messes at page and column breaks. The quotes should therefore be placed after the text is finished.