But Schwimmer has said that the reports are completely false.
Schwimmer was quoted in the British press as saying that the ninth series of the show, due to begin filming later in the summer, would be the last.
But Schwimmer has said that the reports are completely false.
"Mr Schwimmer never made the statement or implied it in any of his interviews while promoting the upcoming mini-series Band of Brothers," said a statement from his PR agency.
Schwimmer plays one of the six core characters in the show, following the lives of a group of New York 20-somethings.
The show's first episode aired in September 1994. It is shown in the UK on Channel 4 and the E4 digital channel.
Online poll
A BBC News Online poll has indicated that the loss of the long-running series would be less than catastrophic for viewers.
Some 66% of respondants felt that it was time for the Friends to go their separate ways.
And only 33.8% wanted to see more of Ross, Joey, Chandler, Rachel, Monica and Phoebe.
More than 7,000 people took part in the vote.
Critics have said the series has been losing its touch of late.
Some of the actors, most notably Lisa Kudrow who plays Phoebe, have burgeoning film acting careers. Her movies include Romy and Michele's High School Reunion and The Opposite of Sex.
Jennifer Aniston's movies include Office Space, The Object of My Affection and Picture Perfect.
Schwimmer is to be seen playing Captain Sobel in Steven Spielberg's World War II TV blockbuster Band of Brothers.
Matthew Perry (Chandler) has had some film roles but achieved greater notoriety for his well-publicised battle with painkiller addiction.