The 24-year-old limped off in the first half of the 1-0 defeat of fellow strugglers Reading on December 8 with a knee complaint, after Royals midfielder Jay Tabb accidentally fell onto him.
Adkins was peppered with questions about the issue throughout a 15-minute press conference this afternoon, saying that Lallana was "progressing well".
However, he staunchly refused to detail how long the player would be out for.
"Adam is still in his knee brace," he said. "He is progressing well and is now off the crutches.
"He won't be available for Saturday's game against Sunderland and that is all I need to say."
Asked for further clarification, Adkins added: "That is all we are going to say.
"We're just going to say he is out for the Sunderland game and you can ask me the next question ahead of the next game."