The singer was just 19 when Supergrass appeared on the list. His solo album, Matador, is more introspective and experimental than his Britpop band.
Other artists nominated for the £20,000 prize include Florence + The Machine, Jamie xx and Wolf Alice.
The winner will be revealed live on BBC Four and BBC 6 Music next month.
There are only two bands in the shortlist, which leans heavily towards singer-songwriters making intimate, confessional music.
Bookmakers' favourites Everything Everything failed to secure a nomination, with other notable absentees including Blur, Laura Marling, Foals and New Order.
Lauren Laverne, who revealed the shortlist on her BBC 6 Music show, said: "It's the perfect snapshot of where music is right now and where it might be heading in the future."
The full list of nominees:
Analysis - Mark Savage: Music reporter
Three singer-songwriters sit on the panel for this year's Mercury Prize, and their influence shows. The list favours solo artists making intimate, confessional albums.
Benjamin Clementine, who has been called "the male Nina Simone" sings about his experiences of homelessness, while Florence + The Machine confronts her personal demons on what is (for her) a subtle, restrained record.
Only two bands make the shortlist - Slaves and Wolf Alice, who represent two opposing approaches to rock. The former are a spittle-flecked burst of raw aggression, while Wolf Alice are sonically adventurous, expansive and destined for an arena near you.
Altogether, the 12 albums are of unusually high quality, and predicting a winner is a fool's errand - but my personal favourite is currently Eska Mtungwazi's beguiling, unpredictable debut, which pulls off the trick of being musically intricate while still sounding organic and free.
Edinburgh-based hip-hop trio Young Fathers won last year's award, while other recent winners have included James Blake, Alt-J, PJ Harvey and The xx.
The prize is judged by a panel of 12 critics, DJs, musicians and other industry figures who often use the shortlist to champion left-field choices as well as more obvious contenders.
Among the less well-known acts this year are Benjamin Clementine, a British-Ghanaian singer who went from busking in Paris to being championed by Sir Paul McCartney, after a fortuitous appearance on BBC Two's Later... With Jools Holland.
Soul-jazz musician Eska also makes the list with her self-titled debut record, after working as an arranger and session singer on three previous Mercury-nominated albums.
Former Moloko star Roisin Murphy gets her first Mercury nomination for the twisted disco of her solo album, Hairless Toys, while electronic musician Aphex also makes his debut on the shortlist with Syro, his first album in 13 years.
Rock band Wolf Alice said they were "flabbergasted" to be nominated for their debut album, which peaked at number two in the UK charts over the summer.
"This has been the best year of our lives," said singer Ellie Roswell. "We're like four excitable kids all the time, having fun. But I'm sure we'll crash and burn shortly."
Several former nominees are on this year's judging panel, including Corinne Bailey Rae, Anna Calvi and Nick Mulvey, alongside a selection of music journalists and broadcasters.
Simon Frith, chair of the judges, said this year's shortlist "celebrates artists from every stage of their careers.
"These musicians come from a fascinating variety of musical places, cultures and histories.  What they have in common is the ambition and the craft, the ideas and the imagination to make great music."
The winner will receive their prize on 20 November, at a ceremony in the BBC's Radio Theatre in central London. The nominated acts will appear throughout the day on the BBC's music stations in the build-up to the show.
Former Supergrass frontman Gaz Coombes has been nominated for the Mercury Music Prize, 20 years after his band's debut album made the shortlist.