The former British and Irish Lion, 30, has been sidelined with a neck injury that has put serious doubt on his World Cup hopes.
“Can he go forward? Or do we need to make a decision that the best thing for him is to relieve the pain and get an operation,” Gatland commented.
“Matthew desperately wants to go to the World Cup but not at the risk of your health and particularly not having a long-term serious neck injury so we must make sure we're smart.”
The prop has received a pain-killing injection for the injury, but the need for an operation that would rule him out until next year’s Six Nations tournament is looking increasingly likely.
Rees’s injury makes up one third of Wales’s front row injury woes, with fellow former Lions Adam Jones and Gethin Jenkins both facing a race against time to get match fit before next month’s tournament in New Zealand.
Jones is understood to have recovered from the toe injury that has so far ruled him out of Wales’s World Cup warm-ups, while Jenkins could return to action this weekend against Argentina following lengthy calf problems.
Gatland will name his 30-man World Cup squad on 22 August.