use strict;
use warnings;

my $MATCH_THIS = q(aa);
my @filenames = qw(file1:aa file2:bb file3:cc file4:AA);

for my $fn (@filenames) {
    print "Matched $fn\n" if $fn =~ /$MATCH_THIS/i;
}
[download]

prints:

Matched file1:aa
Matched file4:AA
[download]

However, from the word 'In' in your post, I get the feeling that you want to grep the content of the files named aa, bb etc. That's not the case, is it?

Update: Added "the content of" for clarification.
Update: Changed @array to @filenames.