Here's an alternative that matches your specs without using eval:

sub check_logs
{
   my $regx_template = shift(@_);
   my @clients = qw(abc def hij);
   foreach my $client (@clients) {
      my $regx = $regx_template;
      $regx =~ s/\\\$(?:client\b|{client})/$client/g;
      print($regx, "\n");
   }
}

foreach my $regx_template (
   qr/pre-\$client-post/,
   qr/foo-\$client-bar/,
   qr/moo\${client}moo/,
) {
   check_logs($regx_template);
}

__END__
output
======
(?-xism:pre-abc-post)
(?-xism:pre-def-post)
(?-xism:pre-hij-post)
(?-xism:foo-abc-bar)
(?-xism:foo-def-bar)
(?-xism:foo-hij-bar)
(?-xism:mooabcmoo)
(?-xism:moodefmoo)
(?-xism:moohijmoo)
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