The former Beatle, who got engaged to the US heiress in May, will exchange vows at London's Westminster Register Office in front of just 30 friends, according to The Mirror.
The pair will then apparently host a low-key reception in the garden of McCartney's home in St John's Wood, London.
"It will be a really special, intimate ceremony followed by a fun do under a marquee in the garden," a source said.
"The wedding is in keeping with the way Paul and Nancy have conducted their entire relationship - low-key, understated and fuelled by goodwill. Neither of them wanted a huge fuss made and the main priority, for both, was family."
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The insider added: "They have chosen a fairly spectacular wedding cake, and ordered a chocolate one for the younger guests. Paul's daughter, Stella, was instrumental in helping choose an entirely vegetarian, mostly organic, three-course sit-down meal.
"The pop-up bar will be free-flowing and Paul keeps threatening to get the guitar out, and dedicate a couple of songs to his new wife."
McCartney's daughter Beatrice is said to be the sole bridesmaid and flower girl, while the singer's brother Mike will oversee proceedings and serve as best man.
The day of the ceremony would have been the 71st birthday of McCartney's late bandmate John Lennon.
The singer has been married twice before. He wed first wife Linda in 1969 and later professed that they only spent a handful of nights apart before his spouse's untimely death nearly 30 years later.
Four years after Linda's death, McCartney married model Heather Mills, but their union ended in divorce in 2008.
Scroll through the gallery below for a look at Paul McCartney's various relationships through the years: