The ex-Take That star and his wife, Ayda Field, have been friends with Eugenie and her sister, Princess Beatrice, for several years and will both attend the wedding, according to a report.
Princess Eugenie and Mr Brooksbank are will tie the knot on Friday October 12 at St George’s Chapel in Windsor Castle - the same venue at which Prince Harry and Meghan Markle wed in May.
Along with Williams' five-year-old daughter, Theodora Rose, other flower girls will be three-year-old Princess Charlotte and Maud Windsor, the four-year-old daughter of Lord Freddie Windsor and his actress wife Sophie Winkleman, according to the Mail on Sunday.
Maud Windsor is in the same class as Prince George, the eldest child of Duke and Duchess of Cambridge, at St Thomas’ School in Battersea.
Prince George is due to be a pageboy at the wedding, along with Louis de Givenchy, the son of the JP Morgan banker Olivier de Givenchy and his wife Zoe, it was reported.
The Duke of York announced in February that the couple would marry on Friday, October 12.
Eugenie, the Queen's granddaughter, became engaged to Mr Brooksbank, her long-term boyfriend, in Nicaragua in January.
She is the younger daughter of the Duke of York and Sarah, Duchess of York, formerly Sarah Ferguson. The 27-year-old is one of the Queen's granddaughters and her elder sister is Princess Beatrice of York.
Eugenie is ninth in line to the throne since the birth of Prince Louis, the Duke and Duchess of Cambridge's third child.
After leaving Take That in 1995, Williams achieved significant commercial success as a solo act. During his career he struggled with addiction to alcohol and drugs.
Last year he boasted that he "smoked a spliff in Buckingham Palace" when he headlined the Queen's Diamond Jubilee concert in 2012.