Using a delayed execution assertion, typically used to create recursively matching regexes, I came up with this: 
my $re;
$re = qr/((.)(??{ $re })\2|.)/;
my $s = 'abcdegedfc';
foreach my $i (0 .. length($s) - 1) {
    local $\ = "\n";  # add newline to print
    substr($s, $i) =~ /^$re/ and print $1;
}

[download]
I need a loop, because the regex by itself doesn't search for the longest palindrome, so I added a /^/ anchor to avoid any potential, useless backtacking. It doesn't actually chnage the result.

This little program prints: 

a
b
c
deged
ege
g
e
d
f
c
So all you still have to do, is keep the longest match from the loops.

update: I found a second working regex, inspired by holli who came up with the idea to use reverse: 

my $s = 'abcdegedfc';
foreach my $i (0 .. length($s) - 1) {
    local $\ = "\n";  # add newline to print
    substr($s, $i) =~ /((.*).?(??{ quotemeta reverse $2 }))/
      and print $1;
}

[download]
Output is identical to the previous program.

In reply to Re: Try this in Regexp palindrome by bart
in thread Try this in Regexp palindrome by Anonymous Monk

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