The 28-year-old has missed the Hammers' last three games with the injury, and is out of Saturday's trip to Aston Villa in the Barclays Premier League.
Owen underwent stomach surgery at the clinic last weekend to cure a groin problem, and could be fit for England's qualifiers against Estonia and Russia as a result.
West Ham assistant manager Mervyn Day said: "We are hoping we will get a definitive answer very soon about what the problem is and how long it will take to fix.
"If we get the same answer Michael Owen and Newcastle got then we will be very happy, because Owen was tipped to recover in eight to 12 days.
"I can't see Craig playing for Wales, though. It's something for our manager Alan Curbishley to discuss with Welsh boss John Toshack, but I think he is very doubtful."