Prince Harry launched mental health charity Heads Together with his brother Prince William last May.
And this week is World Mental Health day, so the duo will be hosting an event in London as well as attending a reception at Buckingham Palace, according to the Daily Star.
Prince William and Prince Harry announced a £2million investment fund to help improve the nation’s mental health through technology yesterday, a reflection of how dedicated they are to raising awareness and their charity.
Meghan and Harry have already made their first official public appearance at the Invictus Games in Toronto.
So it would be the perfect way for the couple to show their increasing seriousness for each other if they made another appearance in the UK.
Attending an event with Prince William and the Duchess of Cambridge would also lessen the pressure on the happy couple.
Prince Harry has a busy week ahead of him, as he is presenting awards to organisations who have supported members of the Armed Forces on Monday.
He will then attend a reception and gala dinner in aid of WellChild on Wednesday.
His week will end by collecting a posthumous Attitude Legacy Award on behalf of his mother Diana, Princess of Wales on Thursday.
If Meghan does join him at on Tuesday or at any of his other appointments this week, it will further intensify speculation the couple are soon to announce an engagement.
Rumours continued to swirl this week after an insider revealed the Suits actress is considering giving up her biggest role to date so that she can move to be with Harry.
Thanks to his royal duties, Prince Harry has to stay in the UK, so Meghan would have to quit her role in the law drama for their relationship to move to the next level.
Speaking to The Sun, the source said: “Meghan loved playing Rachel and feels she owes so much to Suits.
“But Harry can’t move to Toronto, so she’ll have to move eventually if they want to be together.
“Her decision to give up the biggest role of her career would mean a lot.”
The couple currently conduct their relationship long-distance, and have travelled to exotic locations around the globe, such as Jamaica and Botswana to spend time together.