Currently on a six-week 'sabbatical' from royal duties to spend time with her family, the Duchess and Clinton thugged during what was described as something of a "fan girl" meeting on Tuesday, The Daily Mail report said citing sources as saying.
This was the first ever meeting between Clinton and Markle.
Markle's husband Prince Harry and their six-month-old son Archie were also present during the meeting and Clinton, even got to have a cuddle of the royal baby and told the Duchess about Chelsea Clinton's new baby son, Jasper, her third grand-child.
"Both women have a lot of admiration for each other and it was a very sweet, warm meeting," one of the source said, adding that "they are mutual fan girls".
Meghan wrote to Clinton when she was just 11 years old to demand her help in getting a "sexist" advertisement for dishwasher soap taken off the screens.
It is not clear whether she ever got a reply but the budding activist did successfully manage to get the voice over that "women all over America are fighting greasy pots and pans" replaced with the more palatable "people".
Apparently the letter was discussed between the two women during Tuesday's meeting, the sources told The Daily Mail.
During an interview with the BBC this week, Clinton said that she wanted to hug Markle, adding "I feel as a mother I just want to put my arms around her".
The former US First Lady, who has often talked of developing "skin like the hide of rhinoceros" through her decades in the spotlight, added: "I want to tell her (Markle) to hang in there, don't let those bad guys get you down. Keep going, do what you think is right."
The 2016 Democratic presidential candidate is currently on a publicity tour for "The Book of Gutsy Women", co-authored with her daughter, Chelsea Clinton.
It is believed that the meeting might have been arranged with the help of the couple's head of communications, Sara Latham, who worked for Hillary Clinton on her campaign.
( With inputs from IANS )