He made the longlist in 2002 for Who's Sorry Now? and in 2006 for Kalooki Nights, a book he described as "the most Jewish novel that has ever been written by anybody, anywhere."
South African Jewish author Damon Galgut has also made the list for his book In a Strange Room.
Both books, chosen by judges from more than 130 titles, are among 13 now vying for a place on the shortlist, which will be announced in September.
The overall winner of the prize will be revealed on October 12.
Former poet laureate Andrew Motion, head of the judging panel, said all the books were “exceptional”.
“Wide-ranging in their geography and their concern, they tell powerful stories which make the familiar strange and cover an enormous range of history and feeling.”
In 1982 Thomas Keneally won the prize for Schindler’s Ark, which told the true story of a businessman who saved thousands of Polish Jews during the Holocaust.
The book was then adapted by Steven Spielberg into the Oscar winning film Schindler’s List.
