Your delayed-evaluation expression isn't quite right. It won't match palindromes like 'feef' that don't have a central character. You need to make the single dot optional. And if you put the alternation in the middle, you won't match one-character "palindromes".
You can also simplify your search by putting the pattern in a lookahead and doing a while-global match:
$_ = 'abcdegedfc'; # Try it without the g, too.
my $re;
$re = qr/((.)(?:(??{$re})|.?)\2)/;
print "$1\n" while (/(?=$re)/g);
If you change the * to a + in the reverse version, you exclude single-character palindromes. The lookahead while-global trick helps here, too:
$_ = 'abcdegedfc';
print "$1\n" while (/(?=((.+).?(??{quotemeta reverse $2})))/g);
Caution: Contents may have been coded under pressure.
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