However, on Friday the midfielder - believed to have returned to his parent club for treatment - tweeted that he had a scan and the injury was "not as bad as first thought."
He said: "There has been some further investigation in London and I only got the information shortly before the game that it is not as serious as it looked four or five days ago.
"Now I have to speak to Chelsea and maybe we need a third opinion. If it is the case that it's not as serious as we thought then that will be one of the happiest decisions."
Palmer, 20, was ruled out of Town's trip to West Ham United and Wagner said at the time he would be sidelined for "some months" and added he would "definitely not be back in the next six to eight weeks."
On Twitter, Palmer said: "Great news from today's scan, not as bad as first thought. God Is Good. Looking forward to be being back training in the next few weeks."