The keeper, who has not played for Wanderers since August 2016, will finally sever ties with the club at the end of this month.
The former Manchester United man had one forgettable season at Bolton as they suffered relegation to League One in 2015/16 and was then sent out on a series of loans in an effort to subsidise his bumper wages.
Amos went to Cardiff City, Charlton and then Millwall, where he made 15 appearances last season.
Now, with his contract expiring, Amos could be heading back to The Valley, where he helped the South London club into the League One play-off semi-finals in his last spell.
“Ben is one of the ones we are trying to work on,” Charlton boss Lee Bowyer told the South London Press. “But he was on a hell of a lot of money, so it’s just whether he is prepared to go down to what we are going to offer.
“We’re just trying to persuade him – he did a great job for us before.
“He loved it here at the club and the fans took to him.
“He has the experience and has played in the division. He knows what we’re like as a club. It is the perfect fit. We do need some experienced players in that division, for sure.
“Ben is a confidence player. Ben had a rocky start to the season with us and then he got better and better as the season went on.”
Amos was a huge success on loan from United in 2014/15 but his move quickly turned into a nightmare as financial problems set in the following season and his own form faltered.
The departure of Neil Lennon and the arrival of new owners Ken Anderson and Dean Holdsworth spelled an abrupt end to his time at Bolton – even though he had two more years on his contract.
In total, he made 54 appearances, the last of which was in a League Cup defeat at Blackpool.