Help identifying potential malware/attack source?

I have noticed one of my clients sites error log has constant entries like the below:

myclientswebsite.org [Wed Jul 30 12:29:33 2014] [error] [client 71.42.245.139:43348] script not found or unable to stat: /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/include.php
myclientswebsite.org [Wed Jul 30 12:29:33 2014] [error] [client 71.42.245.139:43472] script not found or unable to stat: /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/itil.php
myclientswebsite.org [Wed Jul 30 12:37:45 2014] [error] [client 91.189.183.100:51727] script not found or unable to stat: /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/thumb_editor.php
myclientswebsite.org [Wed Jul 30 12:37:48 2014] [error] [client 91.189.183.100:52927] script not found or unable to stat: /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/include.php
myclientswebsite.org [Wed Jul 30 12:37:48 2014] [error] [client 91.189.183.100:52958] script not found or unable to stat: /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/itil.php
myclientswebsite.org [Sun Aug 03 17:20:53 2014] [error] [client 37.59.44.64:43778] AH01276: Cannot serve directory /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/: No matching DirectoryIndex (index.cgi,index.php) found, and server-generated directory index forbidden by Options directive
myclientswebsite.org [Sun Aug 03 17:20:53 2014] [error] [client 37.59.44.64:43797] AH01276: Cannot serve directory /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/: No matching DirectoryIndex (index.cgi,index.php) found, and server-generated directory index forbidden by Options directive
myclientswebsite.org [Sun Aug 03 17:20:58 2014] [error] [client 37.59.44.64:45265] script not found or unable to stat: /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/thumb_editor.php
myclientswebsite.org [Sun Aug 03 17:21:00 2014] [error] [client 37.59.44.64:46001] script not found or unable to stat: /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/include.php
myclientswebsite.org [Sun Aug 03 17:21:01 2014] [error] [client 37.59.44.64:46010] script not found or unable to stat: /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/itil.php
myclientswebsite.org [Sun Aug 03 17:21:07 2014] [error] [client 70.32.97.96:48312] AH01276: Cannot serve directory /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/: No matching DirectoryIndex (index.cgi,index.php) found, and server-generated directory index forbidden by Options directive
myclientswebsite.org [Sun Aug 03 17:21:07 2014] [error] [client 70.32.97.96:48386] AH01276: Cannot serve directory /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/: No matching DirectoryIndex (index.cgi,index.php) found, and server-generated directory index forbidden by Options directive
myclientswebsite.org [Sun Aug 03 17:21:12 2014] [error] [client 70.32.97.96:50114] script not found or unable to stat: /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/thumb_editor.php
myclientswebsite.org [Sun Aug 03 17:21:15 2014] [error] [client 70.32.97.96:51031] script not found or unable to stat: /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/include.php
myclientswebsite.org [Sun Aug 03 17:21:15 2014] [error] [client 70.32.97.96:51116] script not found or unable to stat: /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/itil.php
myclientswebsite.org [Mon Aug 04 00:35:38 2014] [error] [client 178.188.223.178:33962] AH01276: Cannot serve directory /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/: No matching DirectoryIndex (index.cgi,index.php) found, and server-generated directory index forbidden by Options directive
myclientswebsite.org [Mon Aug 04 00:35:43 2014] [error] [client 178.188.223.178:34877] AH01276: Cannot serve directory /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/: No matching DirectoryIndex (index.cgi,index.php) found, and server-generated directory index forbidden by Options directive
myclientswebsite.org [Mon Aug 04 00:36:23 2014] [error] [client 178.188.223.178:42326] script not found or unable to stat: /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/thumb_editor.php
myclientswebsite.org [Mon Aug 04 00:36:40 2014] [error] [client 178.188.223.178:45890] script not found or unable to stat: /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/include.php
myclientswebsite.org [Mon Aug 04 00:36:46 2014] [error] [client 178.188.223.178:47008] script not found or unable to stat: /home/sites/myclientswebsite.org/public_html/wordpress/wp-content/uploads/2014/02/itil.php

This continues back with different files as far as the log will let me see (June) where there is also a flurry of not found requests for join.php register.php and signup.php in the root installation directory.

I have failed to find any script in the site which shouldn’t be there (ie ones that whatever it is are hitting successfully) and I have run a couple of malware scanning plugins which have also found nothing.

There doesn’t appear to be any dodgy stuff going on with the sites Google results or anything either, this is the only clue I had to any problems.

I am now running iThemes Pro on the site as it wasn’t protected in any way prior but obviously something is either in the site and firing or some external source is weirdly stabbing at malware files that aren’t there.

Does anyone have any ideas what this is and how I can prevent further logged errors?

Thanks in advance