The report added Princess Anne was tipped to replace Harry as Captain General of the Royal Marines. If the move goes ahead, she will become the first woman to have the position.
The Duchess of Cambridge currently holds other sporting patronages - she is patron of the All England Lawn Tennis and Croquet Club, the Lawn Tennis Association, Sports Aid, and the 1851 Trust.
Kate's new patronages will put her in competition with Prince William, who is patron of the Welsh Rugby Union and president of the Football Association.
The Cambridges' competitive sporting spirit was observed when the family attended the Euro 2020 final, with the royal couple's eldest child Prince George appearing heartbroken as Italy clinched the victory in a nail-biting match.
Meanwhile, Harry and Meghan are preparing to celebrate the former actress' 40th birthday party at their Santa Barbara home in California.
The couple, who recently welcomed their second child Lilibet Diana into the world, has reportedly enlisted the help of celebrity party planner Colin Crowe. He counts Jennifer Aniston, Tom Cruise, Kim Kardashian West and Jennifer Lopez among his clients.