The simplest might be to just wrap the \caption in a minipage of a specific (to be determined) height.
Something like:
\fbox{\begin{minipage}[t][5cm][t]{1.0\linewidth}
\caption{This is a short caption}
\end{minipage}}
I added a \fbox to show the size of this minipage. Of couse the 6cm part has to be adjusted and probably best stored in a length such that we don't have to change 6cm by hand al over the pace (left as an excersize).
Below I've added a MWE showing what this looks like. I've also added how one should redefine \cation to do this automatically. This of course assumes \caption is only used in this contrex, that is no figures that are not full page figures, and no tables.
\documentclass[a4paper]{memoir}
\usepackage{kantlipsum}
\begin{document}
sdf % to get to a LH page
\newpage
% \fbox added to show the size of the caption minipage
\begin{figure}[p]
\centering
\rule{0.7\textwidth}{10cm}
\fbox{\begin{minipage}[t][6cm][t]{1.0\linewidth}
\caption{\kant*[1]}
\end{minipage}}
\end{figure}
\clearpage
\begin{figure}[p]
\centering
\rule{0.7\textwidth}{10cm}
\fbox{\begin{minipage}[t][5cm][t]{1.0\linewidth}
\caption{This is a short caption}
\end{minipage}}
\end{figure}
\clearpage
% automatic, assumes \caption are only used in constructions like
% above
\let\normalcaption\caption
% this will loose the [] option for \caption
\renewcommand\caption[1]{
\begin{minipage}[t][5cm][t]{1.0\linewidth}
% now call the normal caption to make the formatting
\normalcaption{#1}
\end{minipage}
}
\begin{figure}[p]
\centering
\rule{0.7\textwidth}{10cm}
\caption{\kant*[1]}
\end{figure}
\clearpage
\begin{figure}[p]
\centering
\rule{0.7\textwidth}{10cm}
\caption{This is a short caption}
\end{figure}
\end{document}

\documentclass{...}and ending with\end{document}. – ebosi May 19 '17 at 16:57floatsthat are positionned with (among other)p(i.e., on a dedicated "float page"). Since there are one float (figure + caption) per page, each of them is vertically centered. // You might want to read How to influence the position of float environments like figure and table in LaTeX? for more details. – ebosi May 19 '17 at 16:59\begin{minipage}[t][6cm][t]{1.0\linewidth}for some yet to be determined length other than 6cm. The[t]part make sure that the alignment inside theminipageis at the top and[6cm]that they all have a height of6cm. – daleif May 22 '17 at 12:49