An aide said he was "looking for opportunities" to highlight and celebrate diversity in both the UK and the Commonwealth.
Although there is no suggestion that he wants to create such an organisation himself, he is said to to be keen to find one that will provide a similar focus to that of the Holocaust Memorial Day Trust.
It was through the trust that the Prince met Eric Murangwa, a Rwandan footballer who narrowly escaped death during the 1994 genocide and urged him to visit memorial sites during his visit to Kigali.
As a result, the Prince and the Duchess of Cornwall last week visited the Kigali Genocide Memorial, noting "how important it is never to forget the horrors of the past."
In a bid to raise awareness of the Windrush generation and mark their "tremendous impact" on the UK, the Prince has commissioned portraits of some of those who travelled from the Caribbean to the UK between 1948 and 1971.
It comes after the Queen officially marked Windrush Day for the first time last week, issuing a personal tribute to the "profound contribution" that the Windrush pioneers and their descendants have made to the UK.
The Duke of Cambridge also acknowledged in a strongly worded speech that the Windrush generation had been "profoundly wronged" and suffered racism in Britain that continues to this day.
The Windrush portraits will be undertaken by artists selected personally by Prince Charles, including several black artists.
It follows similar initiatives in which he commissioned portraits of surviving servicemen to mark the 70th anniversary of the Battle of Britain in 2010, portraits of D-Day veterans in 2015 and portraits of Holocaust survivors in 2020.
The portraits will feature members of the Windrush generation chosen from across the UK by the Windrush commemoration committee. It is hoped they will be shown together for the first time on Windrush Day 2023 in the Queen's Gallery at Buckingham Palace, with the exhibition opened by the Prince.
He said: "The Windrush vessel arrived at Tilbury in the year I was born, inspiring a generation who made this country home.
"I have always thought of the United Kingdom as a community of communities whose strength is in our diversity, and over the last 75 years this generation has made an immeasurable contribution to the society we share. That is why, in this special anniversary year, I wanted to pay my own heartfelt tribute to the role they have played in our nation's story."
The Prince's call for better acknowledgement of the slave trade came after he expressed his deep personal sorrow over the "painful history" of slavery, acknowledging that lessons must be learnt in order for the Commonwealth to move forward.
He told Commonwealth leaders in Kigali on Friday that the roots of the 54-member association "run deep into the most painful period of our history."
He also made it clear that if Commonwealth realms wanted to sever ties with the royal family and become republics, such change could be made "calmly and without rancour".
Campaigners have long argued that black history in Britain cannot be fully understood without a deep understanding of the transatlantic slave trade, often described as one of the greatest crimes against humanity, and its continued role in shaping modern society.
In turn, its impact on the experience of the Windrush generation and their descendants is considered critical.
There have been increasing calls for members of the royal family to apologise for the monarchy's role in financing and perpetuating the slave trade.
The Duke and Duchess of Cambridge faced a confrontation over slavery reparations during their recent Caribbean tour, which was criticised for its colonial overtones.
