You may be able to wrap your script in another script that inserts the print statements for you:

my $script;
while (<DATA>) {
   $script .= $_;
   $script .= qq{print "line $.\\n";\n};
}

eval $script;

__END__

# your script goes here
[download]

You may be able to take this on step further and place that in a package, say, 'FollowLines', and then do something like this:

use FollowLines;

__DATA__

# your script goes here
[download]

Be advised, though, that multi-line constructs will break this. Consider this code:

if ($some_var == 1 ||
    $other_var == 2 ||
    $third_var)
{
    sprintf("%s %s %d %s\n",
        $some_var,
        $other_var,
        @rest);
}
[download]

A print statement every line would be a Bad Thing. I'm afraid there's not much you can do to get this functionality in a reliable fashion.