During a show last night in Perth, Australia, drummer Jon Farris took the mic from latest singer Ciaran Gribbin and told the audience: "This is the last time we will perform together".
They were touring as support to Matchbox Twenty and celebrating the 25th anniversary of their most successful album, Kick.
Despite Farris' announcement, revealed in the Brisbane Times, and his comment about "getting teary" towards the end of the show, the band have not officially confirmed their position.
Just last month Gribbin, who joined last year, said they were working on new material and planned a "big future".
Inxs have faced a series of challenges since the suicide of original frontman Michael Hutchence in 1997. For three years they performed intermittently with guest singers before hiring Jon Stevens, who became a full member in 2002. He left the following year.
In 2004 they became the focus of TV reality show Rock Star: Inxs, in which singers competed to become their new frontman. It was won by JD Fortune, who recorded 2005 album "Switch".
Following a 2009 tour the singer, who admitted he'd become a cocaine addict, told the media he'd been dismissed. The band said he hadn't and indeed, he returned for another stint.
Irish musician Gribbin, who provided backing vocals for Snow Patrol's best-selling album "Eyes Open", was hired last year.
Inxs formed at school in 1977 in New South Wales before the members eventually relocated to Sydney. Midnight Oil manager Gary Morris helped them enter the music business. At his suggestion they took on the band name in 1979. They release their first single, "Simple Simon", the following year.
Thanks to ClassicRockMagazine for the report.