You could define a \foottextcite macro based on \textcite (i.e., with braces).
EDIT: The example now uses style=authoryear-icomp.
EDIT 2: Added code for new option autocite=foottext which maps \autocite to \foottextcite.
\documentclass{article}
\usepackage[style=authoryear-icomp]{biblatex}
% The following is based on \textcite
\DeclareCiteCommand{\foottextcite}[\mkbibfootnote]% [\mkbibfootnote] added
{\usebibmacro{cite:init}}
{\usebibmacro{citeindex}%
\usebibmacro{textcite}}
{}
{\usebibmacro{textcite:postnote}}
\DeclareMultiCiteCommand{\foottextcites}[\mkbibfootnote]{\foottextcite}{\multicitedelim}
\DeclareAutoCiteCommand{foottext}[l]{\foottextcite}{\foottextcites}
\ExecuteBibliographyOptions{autocite=foottext}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@misc{A01,
author = {Author, A.},
year = {2001},
title = {Alpha},
}
@misc{B02,
author = {Buthor, B.},
year = {2002},
title = {Bravo},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\textheight=120pt% only for the example
\begin{document}
Some text \autocite{A01,B02}.
\printbibliography
\end{document}

EDIT 3: For the sake of completeness, here's the \foottextcite definition suitable for authoryear:
% The following is based on \textcite
\DeclareCiteCommand{\foottextcite}[\mkbibfootnote]% [\mkbibfootnote] added
{\boolfalse{cbx:parens}}
{\usebibmacro{citeindex}%
\usebibmacro{textcite}}
{\ifbool{cbx:parens}
{\bibcloseparen\global\boolfalse{cbx:parens}}
{}%
\multicitedelim}
{\usebibmacro{textcite:postnote}}