Cardiff Blues flanker Sam Warburton, who skippered Wales in their defeat to the Barbarians two months ago, is lined up to keep the job at Twickenham next Saturday.
Scarlets hooker Rees led Wales throughout last season's international schedule, including the RBS 6 Nations Championship.
But he has been suffering with a neck injury in recent weeks, and Wales coach Warren Gatland admits surgery is a possibility.
Gatland, though, hopes any operation that might be required would not take place until after Wales' World Cup campaign, which begins against South Africa in Wellington on September 11.
"Matthew has had a bit of a neck problem for a few weeks," said Gatland.
"He is getting injections today, and we're hopeful he will be alright in the next week or two.
"An operation is a definite possibility but we are hoping it definitely won't be before the World Cup. If he doesn't improve, he may need something after the World Cup.
"There is a bit of nerve pressure, and we're hopeful the injections will help. It is mainly affecting him when he is trying to sleep.
"Ideally, you would like him to play in the warm-ups because you don't want him to go in cold.
"He is getting frustrated because he hasn't been able to do much in the last couple of weeks."
Wales will play three World Cup preparation fixtures this month, with a return match against England in Cardiff on August 13 followed by Argentina visiting the Millennium Stadium seven days later.
Gatland intends announcing his final 30-man World Cup squad for New Zealand on August 22.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
$29.99
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.
