The news follows earlier reports that the media group's broadcast and music magazine division Emap Performance is introducing a spate of job cuts to save costs.
Emap's consumer magazines division has declined to comment on the closure of the two titles or to indicate if there will be more job cuts. Emap would only say that the two titles were under review and a decision would not be reached for a number of weeks.
In the latest set of ABC figures, the 24-year-old Face was down 7.8% on the previous six months to 40,286. Its circulation is down 4.6% year on year.
Last month Emap dismissed reports that The Face editor Neil Stevenson was to be axed.
Reports suggested that the founder was to be turfed out over declining sales at the Emap style bible and because of the magazine's "relentless plugging" of Popbitch, the internet gossip column that Stevenson's girlfriend still runs.
It is thought that the publisher will consider a number of options such as different formats or selling the title off. Emap bought the title along with Arena for £16m in 1999 from Wagadon, and in the same year its circulation dropped from 71,000 to 40,000.
The first issue of The Face in May 1980 featured The Clash, Madness and Dexy's Midnight Runners. In recent years it has been accused of losing its edge.
In its early days, the magazine was widely regarded as a backlash to Thatcherism. It has helped to launch the career of supermodel Kate Moss and widely documented the likes of punk, acid house and Britpop over the decades. The latest cover features designer John Galliano and model Giselle.
J-17, the other title at the top of Emap's crisis list, is losing the battle against teen websites and increasing competition. Its circulation is down to 134,650, a decline of 6% year on year.
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