The 47-year-old has refused to discuss the captain's problem, other than ruling him out of this weekend's fixture against Sunderland and that he will continue to wear a knee brace
The midfielder has been ruled out of this weekend's clash with Sunderland and will continue to wear a knee brace but Adkins has refused to put a date on his comeback.
He told reporters: "Adam is still in his knee brace. 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."
Adkins has revealed he will be a miss for the team but has stressed his side have the players to fill in for him whilst he recovers.
He continued: "He is obviously the captain of the team, an instrumental character. He has got in the England set-up this season but we've got other players as well.
"Gaston Ramirez played there ever so well there when we played Reading, but we've got several players that can play in that position as well.
"Like all teams, you are going to suffer from injuries at certain stages, it is how well you can deal with it.
"I believe we have got several very good players that can play in offensive positions, especially where Adam plays."
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Fellow midfielder Jack Cork was more forthcoming when it came to discussing Lallana's injury and appeared to play it down.
He said: "Adam hasn't trained this week and it is up to the manager if he plays this weekend or not.
"We will just have to see what the manager is thinking about Adam."
Lallana is Adkins' only worry as Frazer Richardson, Richard Chaplow and Paulo Gazzaniga have recovered from their injuries leaving the manager with a difficult choice over who to play in goal.
He added: "Paulo has been on the training ground. Today he had a proper training session.
"Kelvin [Davis] played against Reading because Paulo was out injured. He came in and did very well.
"He kept a clean sheet and put a good performance in so we've got good competition for places and that is important."