You can set the position with xlabel style={at={}}
. The left of the plot is current axis.left of origin
.
MWE:
\documentclass{article}
\usepackage{pgfplots}
\begin{document}
% http://pgfplots.sourceforge.net/gallery.html
\begin{tikzpicture}
\begin{axis}[
axis lines = middle,
xlabel = {x label},
xlabel style={at={(current axis.left of origin)},anchor=south west},
ylabel = {y label},
x dir = reverse, % <-- Important
]
% use TeX as calculator:
\addplot {x^2 - x +4};
\end{axis}
\end{tikzpicture}
\end{document}
Result:

Source: PGFPLOTS manual section 4.9.9 Axis Lines.