A statement on Charlton's website read: "The investor group is undertaking full legal and financial due diligence.
"Subject to them being satisfied with the outcome, it is anticipated that completion of the acquisition will take place no later than 24 December."
The League One club turned down a takeover bid by Swiss-based fund manager Sebastien Sainsbury, a member of the supermarket dynasty, in November.
I'm glad it is someone who knows and loves the club but do they really have a decent amount of money? Jseyaddick6 Lifelong Addicks fan Murray restructured the club during the summer when Charlton Athletic plc was effectively wound up over debts of more than £30m and made it known that they needed new investors.
Varney, who is also a long-standing Charlton supporter, was chief executive from 1997 until 2008 and he stayed on after that to help them find new investment.
The club statement added: "Baton 2010 Limited has accepted an indicative and legally binding offer for the acquisition of Baton 2010, Charlton Athletic Football Company Limited and Charlton Athletic Holdings Limited from an investor group represented by former Addicks chief executive Peter Varney."