The deal was supposed to have be completed on Christmas Eve.
"It wasn't our fault, but during the Christmas holidays it's not easy to do a transaction," Varney told BBC Sport. "Talks are now very advanced."
He continued: "Charlton's finances are not in a good state and the fans can rest assured that this is in the best interests of the club."
Charlton is still owned by a company called Baton 2010 Limited, which is controlled by club chairman Richard Murray and his family.
On 3 December the Addicks confirmed that lifelong fan Murray had accepted a 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 Varney.
The club said in a statement: "It is anticipated that completion of the acquisition will take place no later than December 24".
With due diligence continuing throughout the month, on Christmas Eve the south Londoners said that "work on the proposed acquisition of the club is continuing".
The identity of the investors Varney is representing is shrouded in secrecy, but their bid is just the latest twist in Charlton's ownership saga.
In November, BBC Sport revealed that the League One had rejected a takeover bid from a group led by Swiss-based fund manager Sebastien Sainsbury.
Murray was forced to restructure the football club in the summer when Charlton Athletic plc was effectively wound up with debts of more than £30m.
I'm glad it is someone who knows and loves the club. But do they really have a decent amount of money?
Jseyaddick6
Charlton Athletic Football Company, which owns the players, and Charlton Athletic Holdings, which owns the Addicks' stadium The Valley and the training ground, were transferred to Murray's new company in July.
Murray has made no secret of the fact the south London side need to find new investors and he recently told a meeting of shareholders in the now worthless plc that £5m is required this season to avoid administration.
After seven consecutive seasons in the Premier League, the Addicks were relegated to the Championship at the end of the 2006-07 campaign and went down to League One in May 2009.
The club have been the subject of considerable takeover speculation over the last three years.
In October 2008, they received an offer from Dubai-based consortium Zabeel Investments but the deal collapsed soon after, and in 2009 they were linked with a bid from former Newcastle United colleagues Dennis Wise and Tony Jimenez.
Charlton were condemned to a second season in English football's third tier when they lost a play-off semi-final to Swindon Town.
Despite this setback and the club's debts, Charlton remain a relatively attractive proposition to investors as the side's famous ground, The Valley, has been extensively modernised over the last decade and boasts a capacity of 27,000.
They also have a recently refurbished training ground and a potential fan base that is only going to grow thanks to London 2012-related regeneration and government plans to build thousands of new homes in the wider area.
The disappointment of May's play-off defeat appeared to carry over into this campaign but the side managed by Phil Parkinson have improved in recent weeks and are now fourth in the table.
Source: BBC Sport
Source: BBC Sport