The books, to be published this month, conclude that the 27- year-old guitarist was deliberately drowned in the swimming pool of his country mansion by one of his aides. Both name a builder, Frank Thorogood, who died last year, as the man responsible for the killing at the star's home at Cotchford Farm, Sussex, on 2 July 1969.
An inquest recorded a verdict of death by misadventure, assuming that Jones - who was notorious for his rock-star excesses - had drowned because of the drink and drugs he had been consuming in the weeks after he was sacked from The Rolling Stones.
But after extracts from the books were published in the People and the News of the World, Sussex Police said they would consider reopening the case.
''Further to articles which appear in the Sunday newspapers, we will look at any new evidence that is brought to our attention,' Det Supt Brian Foster said.
Paint It Black by Geoffrey Guiliano and Terry Rawlings' Who Killed Christopher Robin? - Cotchford was once the home of A A Milne, author of the Winnie the Pooh books - claim to have unearthed fresh evidence about Jones's final hours which proves he was deliberately killed. Mr Guiliano's book quotes an unnamed associate of Mr Thorogood's, described as 'a burly Cockney', who admits helping him hold Jones's head under the water in the pool.
Mr Rawlings' book, which says Mr Thorogood carried out the murder alone, is based on a deathbed confession he was said to have made to his friend Tom Keylock, the former Stones road manager.
The two books broadly agree that shortly before he died, Jones had argued with Mr Thorogood, who was supposed to supervising building work at his home, accusing the builder of cheating him out of thousands of pounds.