The 38-year-old, who is now out of contract, missed almost all of last season after breaking his foot in the opening day clash against Plymouth.
Chambers still hasn’t fully recovered from that injury.
And the midfielder, who has been Walsall’s club captain for the past five years, is currently understood to be considering his options – which includes the possibility of retirement.
Clarke has spoken to Chambers a number of times over the summer. And he says an offer to join training will remain on the table for the midfielder who has appeared for the Saddlers more than 300 times.
“I have spoken to Adam and there is an offer open if he wants to continue playing,” Clarke said.
“But he is injured. He is welcome at the club and for me to assess him.
“But I don’t know what Adam is planning. I have told him to pick up the phone if he is ready to stay in football and have a go.
“If he wants to come in he will be assessed as a trialist.”
Despite rumours to the contrary, Walsall haven’t made an offer that would see Chambers join the coaching staff.
“There is no coaching role for Adam,” Clarke added.
“I’m not sure where he wants to take his career at the minute. He is still having problems with his foot.”
Chambers, who was born in Sandwell, began his career with Albion.
He joined Walsall in 2011 following five years at Leyton Orient.
His twin brother James, who played for Walsall between, retired in 2015.