The out-of-contract 38-year-old is yet to fully recover from the foot injury sustained on the opening day of last season and is understood to be considering his options, including the possibility of retirement.
Chambers has made more than 300 appearances since joining the Saddlers in 2011 and been club captain for the past five years. An invite to attend pre-season training remains on the table.
Clarke said: “I have had a couple of conversations with Adam and we’ll see how that develops.
“There is no rush. He is out of contract and it was a case of him being welcome to come into pre-season to have a look and see where his fitness levels are. He has been a great servant to the club and it was a respectful thing for me to do. The door is open if he wants to come in and do some training.”
The Saddlers returned to pre-season training on Monday and Clarke said: “It’s been really good. We are back nice and early and have a six-week pre-season programme in place.
“It’s been nice to meet the lads face to face. As you would expect the attitude has been spot on - but is has only been a day. I had spoken to most of them anyway but it is nice to get them out there and see them working.
“I have made things crystal clear on how we are moving forward. The response has been very good. I knew it would be.”