The Addicks are looking for their third boss of the season having sacked Michael Appleton following Tuesday night's 3-2 defeat at home to Northampton.
It has left them four points away from the relegation zone in a season that many fancied Charlton as potential promotion chasers.
But the dismissal of Appleton means that the London side are now looking for a fourth manager in 14 months.
He took over from Dean Holden in September, who was sacked days before in August after just one win in six at the start of the season.
The former Blackpool and Portsmouth boss oversaw a run of 12 matches without a win while he took charge of just 28 games in total.
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"Charlton Athletic can confirm that Michael Appleton has left the club with immediate effect after being relieved of his role as head coach," a short statement read from Charlton, just 30 minutes after defeat to Northampton Town.
"The club would like to thank Michael for his efforts during his time in charge."
And in line to replace him could be Welshman Jones, who's been out of work since being sacked as Southampton boss in February 2023.
The 50-year-old has plenty of experience having managed in the Premier League and Charlton fans will be encouraged by his work with Luton.
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He took them from League Two to League One and was also in charge of them in the 2018/19 season, where he left to become Stoke boss, which saw them earn promotion to the Championship.
But saving Charlton from relegation to the fourth tier of English football for the first time in their history could be the biggest challenge yet for Jones.