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

Is Prince Harry already thinking about proposing to Meghan Markle?

"That is certainly a possibility," one friend told PEOPLE. "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 going so well between the two that Harry has already introduced Markle to his father, Prince Charles, PEOPLE reports.

They are both getting very serious about each other and have a lot in common. Markle is probably enjoying Harry's romantic side. "He is the sort of man who will send flowers,"says royals author Ingrid Seward. "He really does wear his heart on his sleeve."

Markle, a Northwestern University grad, has possibly been posting clues on her Instagram about this relationship over the last few months. She just shared a photo on Tuesday of two cuddling bananas.

The prince's office does not comment on "private matters," while Markle's representatives have not yet commented on the relationship.