Referencing a quote environment

See below for Alternate Appearance. See ADDENDUM for version that uses aux file to allow future referencing

As Christian noted in a comment, a quote has no counter (and thus no identifying label). However, we could introduce one to the lquote environment, which requires a label as the argument, reference-able by \quoteref.

The implementation given below can be altered to suit the needs for quotation marks, numbering scheme and appearance, etc.

\documentclass{article}
\newcounter{numquote}
\newenvironment{lquote}[1]{%
  \stepcounter{numquote}%
  \expandafter\xdef\csname#1\endcsname{\fbox{\thenumquote}}%
  \quote``\ignorespaces}{\unskip''\fbox{\thenumquote}\endquote}
\newcommand\quoteref[1]{\csname#1\endcsname}
\begin{document}
Compare this quote
\begin{lquote}{quote:one}
blabla
\end{lquote}
to this one
\begin{lquote}{quote:two}
moreblabla
\end{lquote}
In quotation \quoteref{quote:one}, we see a difference from quote \quoteref{quote:two}.
\end{document}

enter image description here

Alternate Appearance

\documentclass{article}
\newcounter{numquote}
\newenvironment{lquote}[1]{%
  \stepcounter{numquote}
  \expandafter\xdef\csname#1\endcsname{\thenumquote}%
  \quote Quote \thenumquote: ``\ignorespaces}{\unskip''\endquote}
\newcommand\quoteref[1]{\csname#1\endcsname}
\begin{document}
Compare this quote
\begin{lquote}{quote:one}
blabla
\end{lquote}
to this one
\begin{lquote}{quote:two}
moreblabla
\end{lquote}
In quotation \quoteref{quote:one}, we see a difference from quote \quoteref{quote:two}.
\end{document}

enter image description here

ADDENDUM:

It seemed from the OP's comment that he may be using the \quoteref prior to the label definition in the lquote environment. To account for that, I have in this addendum implemented a system of writing out to the aux file to make the labels available even before they are defined.

\documentclass{article}
\makeatletter
\long\def \protected@iwrite#1#2#3{%
     \begingroup
     \let\thepage\relax
     #2%
     \let\protect\@unexpandable@protect
     \edef\reserved@a{\immediate\write#1{#3}}%
     \reserved@a
     \endgroup
     \if@nobreak\ifvmode\nobreak\fi\fi
    }
\newcounter{numquote}
\newenvironment{lquote}[1]{%
  \stepcounter{numquote}%
  \protected@iwrite\@auxout{\def\nex{\noexpand\noexpand\noexpand}}{%
    \nex\expandafter\xdef%
    \nex\csname #1%
    \nex\endcsname{\thenumquote}%
  }%
  \quote Quote \thenumquote: ``\ignorespaces}{\unskip''\endquote}
\makeatother
\newcommand\quoteref[1]{\csname#1\endcsname}
\begin{document}
In the future quotation \quoteref{quote:one}, 
  we see a difference from quote \quoteref{quote:two}.

Compare this quote
\begin{lquote}{quote:one}
blabla
\end{lquote}
to this one
\begin{lquote}{quote:two}
moreblabla
\end{lquote}
In quotation \quoteref{quote:one}, we see a difference from quote \quoteref{quote:two}.

\end{document}

enter image description here


Note: the \protected@iwrite macro came from egreg's answer at Writing \\ to a File.