I used the following code from Numbering enumerate environments and pages with Devanagari alphabet to generate अ, आ, इ, ई, etc. as page numbers in the \frontmatter.
\makeatletter
% Always use Devanagari consonants for alph/Alph/roman/Roman styles.
\def\devanagari@alph#1{%
\ifcase#1\or अ\or आ\or इ\or ई\or उ\or ऊ\or ए\or ऐ\or ओ\or औ\or
\else\@ctrerr\fi}
\let@alph\devanagari@alph
\let@Alph\devanagari@alph
\let@roman\devanagari@alph
\let@Roman\devanagari@alph
\makeatother
I customized it by replacing the word 'devanagari' with 'kannada' ...
\makeatletter
% Always use Kannada vowels for alph/Alph/roman/Roman styles.
\def\kannada@alph#1{%
\ifcase#1\or ಅ\or ಆ\or ಇ\or ಈ\or ಉ\or ಊ\or ಋ\or ಋ\or ಎ\or ಏ\or ಐ\or ಒ\or ಓ\or ಔ\or ಅಂ\or ಅಃ\or
\else\@ctrerr\fi}
\let@alph\kannada@alph
\let@Alph\kannada@alph
\let@roman\kannada@alph
\let@Roman\kannada@alph
\makeatother
... and got the desired result!!
Very grateful to @ShreevatsaR for your wonderful code snippet along with a nice explanation.
This is my MWE:
\documentclass{book}
\usepackage{polyglossia}
\newfontfamily\kannadafont{Noto Sans Kannada}[Script=Kannada]
\setmainlanguage[numerals=Kannada]{kannada}
\makeatletter
%---
\def\kannadadigits#1{\expandafter@kannada@digits #1@}
\def@kannada@digits#1{%
\ifx @#1% terminate
\else % ೦೧೨೩೪೫೬೭೮೯
\ifcase#1೦\or೧\or೨\or೩\or೪\or೫\or೬\or೭\or೮\or೯\fi
\expandafter@kannada@digits
\fi
}
%---
\def\kannadanumber#1{%
\kannadadigits{\number#1}%
}
%---
\let@arabic\kannadanumber%
%---
\makeatother
\makeatletter
% Always use Kannada vowels for alph/Alph/roman/Roman styles.
\def\kannada@alph#1{%
\ifcase#1\or ಅ\or ಆ\or ಇ\or ಈ\or ಉ\or ಊ\or ಋ\or ಋ\or ಎ\or ಏ\or ಐ\or ಒ\or ಓ\or ಔ\or ಅಂ\or ಅಃ\or
\else@ctrerr\fi}
\let@alph\kannada@alph
\let@Alph\kannada@alph
\let@roman\kannada@alph
\let@Roman\kannada@alph
\makeatother
\begin{document}
\chapter{ಕನ್ನಡ}
\section{ಕನ್ನಡ}
ಕಖಗಘ
\subsection{ಕನ್ನಡ}
ಕಖಗಘ
\kannadanumber{132 456 987}
೦೧೨೩೪೫೬೭೮೯
\section{ಕಖಗಘ}
\today
\subsection{ಕಖಗಘ}
\section{ಕಖಗಘ}
ಕಖಗಘ\footnote{ಕಖಗಘ} ಕಖಗಘ\footnote{ಕಖಗಘ} ಕಖಗಘ\footnote{ಕಖಗಘ}
\end{document}
Thanks @Cicada for the code snippet which brings in Kannada Numerals instead of the arabic ones. Please excuse me if something is wrong with the Kannada words. I cannot read the language.