Executives at the broadcaster were rumoured earlier this week to be keen to secure further episodes of the popular sitcom, which satirises celebrity culture, fads and fashion trends, after the success of two specials over the Christmas period.
The two new episodes, which broadcast on Christmas Day and New Year's Day, achieved audiences of 7.43 and 7.12 million viewers respectively, and were the first appearances made by the characters since the previous episode, White Box in 2004, and a brief Comic Relief appearance in March 2005.
The ratings and critical success of the episodes has lead bosses to ask Jennifer Saunders to write a further Christmas special for 2012, and a full series, which would air in 2013. The British Comedy Guide understands that the BBC is now waiting for her response.
On Tuesday, the Daily Express newspaper reported a BBC insider as saying: "The viewing figures prove it's as popular as ever and there's a real appetite for more episodes. Obviously it's down to Jennifer to write more and getting all the actors together takes some organising."
The two specials - and a third Olympics-themed episode, due to be broadcast later this summer - were recorded in August last year, to mark the 21st anniversary of the series. Originating as a sketch in an episode of the French & Saunders sketch show, it ran for 3 series and a two-part 'final' special between 1992 and 1996, before being revived for 2 further series and a number of additional specials from 2001 to 2005.
However, any new series could clash with plans to produce a film adaptation of the sitcom. Saunders has made clear on her Twitter account that she is very keen to pursue the big-screen project, and there have been rumours that it would be based around the French Riviera. Whilst a new TV series and the film could not be physically produced at the same time, it is possible that the agreement for one could include a development deal for the other.
Absolutely Fabulous is a co-production between the BBC and Saunders' production company, Saunders & French Productions. The 3 new episodes have been produced in association with BBC America and American cable channel Logo, which caters for LGBT audiences.
The following video is from the Christmas Day special, Identity: