I think the code below looks cleaner. Depending on what your code does, you can use the memoize module to keep a cache of files you have already checked. Passing $dir_path and $filepath to the subroutine is definitely a good idea. My point here is that it is best to keep subroutines self-contained and not use external variables:

use strict;
use Memoize;
memoize ('read_files');
sub process_files
{
    my $dir_path = shift;
    if (opendir(TEST, $dir_path))
    {
        my @files = sort grep{$_ ne '.' and $_ ne '..'} readdir(TEST);
        #print "\n@files[0]\n";
        read_files("$dir_path\\$_") foreach (@files);
    }
    else
    {
        die ("Could not Opendir $dir_path: $!\n");
    }closedir TEST;
}
sub read_files 
{ 
    my $file_path = shift;
    if (-f $file_path)
    {
        print (DATA "$file_path\n") if ($file_path !~ /(\.lfa|\.zip|\.
+txt|UASTG)$/);
    }
    else
    {
        die ("Could not open[$file_path], $!\n");
    }
}
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The only global here is the DATA filehandle, but you should pass that along through the subroutine chain as a parameter.
-imran