Following reports of a comeback in April, new rumours emerged this week that the band would reform in 2013 and play a headline set at the Glastonbury festival.
"The Smiths are never, ever, ever, ever, ever, ever, ever, ever going to reunite - ever," Morrissey's publicist told Rolling Stone.
Marr's manager Joe Moss added to NME :"It isn't happening. We are fully focussed on preparing Johnny's new album for release and booking shows for 2013."
The Smiths split in 1987 and following the break-up Mike Joyce and Andy Rourke took Morrissey and Marr to court in a dispute over royalties. Morrissey's appeal against the verdict in favour of Joyce was dismissed.
After the split but before the court case, Morrissey recorded several solo tracks with Rourke, Joyce and The Smiths' occasional live rhythm guitarist Craig Gannon, including 'Interesting Drug'.
In January 2006, Rourke joined Johnny Marr and The Healers on stage for a performance of The Smiths' 'How Soon Is Now?' at the Manchester v Cancer benefit concert.
Morrissey has released nine solo albums, the most recent being 2009's Years of Refusal.
Rourke has recorded music with bassist collective FreeBass, while Joyce now guest DJs on BBC 6 Music.
Marr recently quipped that he would reform The Smiths if the current coalition government stepped down, prompting Labour's John Prescott to support calls for a reunion.
Reading and Leeds Festival organiser Melvin Benn has suggested that the band reforming would "destroy their legacy", while Marr has said that it would "make so many people happy".
The guitarist denied claims that he had been made an "official offer" of $75m (£47.2m) for a 50-date concert tour with Morrissey in 2007.
Watch The Smiths' 'The Queen Is Dead' music video below: