Will Meghan Markle and Prince Harry See the Royal Family During Their U.K. Visit Next Month?

Meghan Markle and Prince Harry are returning to the U.K. for a series of charity visits next month — raising the prospect that they could meet with their royal relatives.

Relations have been strained between the Duke and Duchess of Sussex and members of the royal family in recent years, including an ongoing estrangement from Prince William and Kate Middleton.

Kate and William will have likely moved into Adelaide Cottage in Windsor by the time Meghan and Harry arrive during the first week of September, which means they will only be a short distance from Harry and Meghan's British home, Frogmore Cottage, which is on the Queen's Windsor Castle estate.

While that could provide a chance for the foursome to get together, there are "no current plans" for the couples to meet up, a source tells PEOPLE.

The Duke and Duchess of Sussex will be in close proximity to Queen Elizabeth as well. Harry's 96-year-old grandmother, who is usually at Balmoral Castle in Scotland during this time of year, is likely to travel back in order to meet with the departing Prime Minister Boris Johnson (and his incoming successor). In her role as head of state, it's also likely she will be called upon to confirm the appointments of Cabinet ministers who will serve in the new government.

Pool/Samir Hussein/WireImage Meghan Markle and Prince Harry

A royal source tells PEOPLE, "There are a lot of moving parts in the diary for the Queen that week."

Palace sources have not said whether those meetings will take place at Buckingham Palace in London or at Windsor Castle.

The couple could also arrive early and travel to Scotland to see Her Majesty ahead of their planned outings. Meghan and Harry are set to be in Manchester for the One Young World Summit on Sept. 5, Germany for the Invictus Games' "One Year to Go" on Sept. 6 and back to the U.K. for the Well Child Awards on Sept 8.

RELATED: Before Harry's Royal Memoir, Learn Whose Palace Tell-All Spilled the Earl Grey Tea First

Seth Wenig/AP/Shutterstock Prince Harry and Meghan Markle

Harry and Meghan were last in the U.K. in June to help celebrate Queen Elizabeth's Platinum Jubilee, but there was no public interaction between the couple and William, Kate and the rest of Harry's immediate family members.

RELATED: See Meghan Markle and Prince Harry's Sweetest Moments at the Invictus Games

They did, however, privately introduce Prince Charles to his granddaughter Lilibet, 1, for the first time, which also gave him the chance to see his 3-year-old grandson Archie, PEOPLE understands.

Samir Hussein/WireImage; Misan Harriman

"It was a fantastic visit. The prince was delighted to see his grandson and meet his granddaughter for the first time," a royal source said, adding that it was "wonderful" to have Harry and Meghan back in Britain.

Lilibet turned one during the family's stay at their Frogmore Cottage home. They also took Lili to meet her great-grandmother, Queen Elizabeth, for the first time. Lili is named for the monarch, as Lilibet was the Queen's childhood nickname.

There is also increasing nervousness in royal circles about Prince Harry's upcoming memoir, which is set for publication later this year. The book follows Meghan and Harry's explosive interview with Oprah Winfrey last year and will cover Harry's childhood in the public eye and his military duty in Afghanistan to becoming a husband to Meghan and father to son Archie and daughter Lilibet.

Samir Hussein/WireImage Meghan Markle and Prince Harry attending the Service of Thanksgiving for the Queen's Jubilee on June 3.

RELATED: Before Harry's Royal Memoir, Learn Whose Palace Tell-All Spilled the Earl Grey Tea First

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"I'm writing this not as the prince I was born but as the man I have become," Prince Harry in a statement about his memoir. "I've worn many hats over the years, both literally and figuratively, and my hope is that in telling my story — the highs and lows, the mistakes, the lessons learned — I can help show that no matter where we come from, we have more in common than we think."