Mouret, a native of France who now calls London home, has remained tight-lipped about whether he has received the commission as Markle's designer.
His recent no comment reply to queries from Women’s Wear Daily about Markle have led many to speculate that Mouret is now the front-runner for the job.
"Mmmmm, I don’t want to say," Mouret told the fashion publication. "There is no comment on that. She’s a friend. And that's ... I can't say."
Mouret is a close friend of Markle, who was living in Los Angeles and Toronto before her engagement to Harry, 33, last November. The friends reportedly met Istanbul years ago.
Markle, 36, once shared that when she first met Mouret he said, "I [would] love to dress you."
"I thought 'What?' Then he told me who he was and we’ve been friends ever since," she recalled.
Mouret's fashion house is based in upscale Mayfair, in an affluent part of London. The designer debuted his first collection at London Fashion week in 1998 and has won numerous British fashion awards.
"Meghan knows really well what she likes and the main thing with Meghan is to listen to her and work in collaboration with her," he recently told the New York Post about Markle, adding, "I’ve already said too much."
Another top contender for designing Markle's gown is the design duo behind Ralph & Russo.
Australian-born designers Tamara Ralph and Michael Russo have already designed for Markle, creating the $75,000 dress she wore in her intimate engagement photos with Harry.
It is typical for designers of royal wedding gowns to remain quiet about their involvement. Sarah Burton, who designed the wedding dress of Princess Kate, denied being the dress designer before Kate and Prince William wed in 2011.
Markle mentioned several designers, including Narciso Rodriguez and Elie Saab, when she spoke to Glamour in 2016 about her dream wedding dress.
She told Glamour that the Narciso Rodriguez–designed white dress that Carolyn Bessette wore to her 1996 wedding to John F. Kennedy, Jr. is her favorite celebrity wedding dress, calling it "everything goals."
Royal watchers expect that Markle will select a designer who either has ties to Britain, her adopted home of Canada or the United States.
There has also been speculation that Markle could choose between two of Princess Diana's favorite designers, Catherine Walker and Amanda Wakeley, who both have couture shops near Kensington Palace.
Both Markle and Harry have said how important it is that Harry's late mother be included in their May 19th wedding, so it would be a sentimental surprise if Markle chose Walker or Wakeley.
Markle is expected to wear two gowns on her wedding day, one for the ceremony at St. George's Chapel at Windsor Castle and a more casual gown for the private evening reception that Harry's father, Prince Charles, is expected to throw for close friends and family.
Her stylist and friend from Toronto, Jessica Mulroney, has been by Markle's side helping guide her through the process. Mulroney flew to London in January to attend Markle's first fitting with her wedding dress designer.