Here, I use a \stackinset, with math style preservation from the scalerel package.
\documentclass{article}
\usepackage{stackengine,scalerel,verbatimbox}
\def\Times{\addvbuffer[-1pt]{$\times$}}
\newcommand\strike[1]{%
{\ThisStyle{\stackinset{c}{}{c}{}{$\SavedStyle#1$}{$\SavedStyle\times$}}}}
\begin{document}
\[A^\strike{\ast} \quad\strike{\ast} \quad
\scriptstyle\strike{\ast} \quad\scriptscriptstyle\strike{\ast}\]
\end{document}

And at the cost of a little more complexity, it can be made to scale to its argument:
\documentclass{article}
\usepackage{stackengine,scalerel,verbatimbox}
\def\Times{\addvbuffer[-1pt]{$\times$}}
\newcommand\strike[1]{%
{\ThisStyle{\stackinset{c}{}{c}{}{$\SavedStyle\scalerel*{\Times}{#1}$}{$\SavedStyle#1$}}}}
\begin{document}
\[\strike{A}\quad A^\strike{\ast} \quad\strike{\ast} \quad
\scriptstyle\strike{\ast} \quad\scriptscriptstyle\strike{\ast}\]
\[\strike{\int_0^B x\,dx}\]
\end{document}

...or throw in a little color with
\newcommand\strike[1]{{\ThisStyle{%
\stackinset{c}{}{c}{}{\color{red}$\SavedStyle\scalerel*{\Times}{#1}$}{$\SavedStyle#1$}}}}

\crin every\ooalignsuperfluous? – campa Aug 12 '15 at 15:03