Two of the books on the list are debut novels - Indian writer Thayil's Narcopolis and Moore's The Lighthouse.
The winner will receive a €50,000 prize, in addition to the €2500 awarded to all shortlisted writers and, importantly, a huge boost in sales for their work. Last year's winner, The Sense Of An Ending by Julian Barnes, has sold more than 300,000 print editions in the UK.
Writers who were on the longlist of 12 but failed to make the final cut are Michael Frayn, Nicola Barker and Andre Brink.
Sir Peter said of the list: "After re-reading an extraordinary longlist of 12, it was the pure power of prose that settled most debates.
"We loved the shock of language shown in so many different ways and were exhilarated by the vigour and vividly defined values in the six books that we chose - and in the visible confidence of the novel's place in forming our words and ideas."
Also among the figures on the judging panel are Downton Abbey actor Dan Stevens, and historian and broadcaster Amanda Foreman.
If Mantel scoops the prize, she will become the first British writer to win it twice.
Sir Peter added: "The judges agree that we have been very fortunate judges. This has been an exhilarating year for fiction. The strongest I would say for more than a decade.
"There are first novels from India and the East Midlands, small publishers from Newcastle, north Norfolk and High Wycombe alongside novels by Hilary Mantel and Will Self, two of the great established radicals of contemporary literature."
One of the books on the shortlist, Levy's Swimming Home, set in a summer villa, was rejected by traditional publishers and only hit the shelves thanks to a publisher which relies on subscriptions from readers.
The judges said they believed that any of the books on the shortlist could end up taking the top prize.
Bookmaker William Hill immediately installed Self as favourite to win the prize after finally being included by the Booker judges following a celebrated career.
He is being given odds of 7/4 to take the prize, with Mantel, whose book is a continuation of her life of Thomas Cromwell, second favourite at 2/1.
If she wins again, Mantel will join an exclusive club, featuring South African-born JM Coetzee and Australian-born Peter Carey, who have won the Man Booker Prize for Fiction twice.
The Garden Of Evening Mists, by Tan who lives in Cape Town, is set in Malaysia during the Japanese occupation.
The Lighthouse, about a middle-aged, recently-separated man who heads to Germany, is by Manchester-born Moore.
Self's book Umbrella is set across an entire century and is described by judges as ``both moving and draining''.
The shortlist comprises:
Deborah Levy - Swimming Home (And Other Stories/Faber & Faber)
Hilary Mantel - Bring Up The Bodies (Fourth Estate)
Alison Moore - The Lighthouse (Salt)
Will Self - Umbrella (Bloomsbury)
Tan Twan Eng - The Garden Of Evening Mists (Myrmidon Books)
Jeet Thayil - Narcopolis (Faber & Faber)
- PAA
