The 25-year-old is out of contract but hooked up with the Addicks for their training camp in Marbella last week.
Williams has already told the South London Press he would like to re-sign for the SE7 outfit after initially joining them in January following his release by Crystal Palace.
“He’s coming in again this week to train with us,” said Charlton boss Bowyer. “It’s just what options Jonny gets, really.
“But we like him. He has come away with us and done really well while we were away. He’s worked hard and looks sharp. He’s definitely one we’re still interested in.
“But it will be a matter of finances regarding Jonny.”
Williams will not play in friendly matches until he has signed for a club.
“Him training with us just makes sense,” said Bowyer. “He lives around the corner and knows everybody.
“He knows he’ll get good training. It means he is ready to go when he does sign for a club.”
Charlton snapped up Ben Purrington from Rotherham last week – with the bulk of the signings still to come.
Bowyer has talked about another seven – with four of those potentially on loan.
“We need a minimum of six,” he said. “We have got to bring in another goalkeeper, that’s for sure, to compete with Dillon. Then it is maybe five or six outfield. I want two players for each position.”
The Addicks paid a fee for a second time this summer to land left-back Purrington. They also spent £200,000 on Leyton Orient striker Macauley Bonne.
“Again the owner has backed us with that,” said Bowyer on the Purrington transfer. “I’m really grateful.
“Ben is a good young player and did well for us this year.
“With Lewis Page as well we have two left-backs in the building. It would be silly to ignore what he could bring to us this season.”
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