Prince Harry Has Already Introduced Meghan Markle to Prince Charles, Engagement 'Certainly a Possibility'

"That is certainly a possibility," a friend of Harry's tells PEOPLE

Prince Harry is so serious with actress Meghan Markle that an engagement could be in the not-so-distant future, insiders suggest.

“That is certainly a possibility,” one friend tells PEOPLE in this week’s issue. “It is certainly one possible outcome. It’s pretty serious, so we will see.”

The prince, 32, and the Suits star, 35, have been dating seriously for about two months, another source confirms. Things are moving so quickly, in fact, that Harry has already introduced Markle to his father (and the future king of England), Prince Charles, PEOPLE has learned.

“Harry is pretty serious about her and she is pretty serious about him,” says the pal. Adds a close friend: “It’s great. They have a lot in common and I’m sure they will get on very well.”

Markle, a Northwestern University grad and the founder of the “inspired lifestyle” site The Tig, has intriguingly posted as series of Instagram clues in recent months—including a cheeky photo on Tuesday of two cuddling bananas.

WATCH: Inside Prince Harry’s Romance with American Actress Meghan Markle

“Harry is quite romantic,” says royals author Ingrid Seward. “He is the sort of man who will send flowers. He really does wear his heart on his sleeve.”

The prince’s office at Kensington Palace says they don’t comment on “private matters,” while representatives for Markle have not responded to requests for comment.

Says Harry’s close friend: “People need to let them go their own way and see what happens.”