Royal expert Katie Nicholl tells ET that the newlyweds are planning to travel to Mexico to pay a visit to see Meghan's father, Thomas Markle, after he was unable to make the royal wedding due to health concerns. If the trip does take place, it will be the first time Harry meets his new father-in-law in person.
"I hear one of the things they want to do sooner than later -- and now that they're married -- is to go and see Thomas Markle, who is recovering from a heart operation," Nicholl says. "We don't know when this trip might happen. ...I'm hearing from people close to Meghan and Harry that they're very keen to do it."
Nicholl adds that it's important to Harry that he know Meghan's dad. "He feels it's very important that he gets to meet Thomas," she notes. "Of course, Meghan -- who's been really concerned about her father's health -- is keen to go see him as soon as possible."
Prior to the royal nuptials on Saturday in Windsor, England, Meghan, 36, revealed that her father would not be attending the wedding after he reportedly had stents implanted in his blood vessels following a heart attack a week prior.
"Sadly, my father will not be attending our wedding," she said in a statement released days before her big day. "I have always cared for my father and hope he can be given the space he needs to focus on his health."
After watching the royal wedding remotely, Thomas spoke with TMZ about what it was like to see his daughter marry a prince.
"The service was beautiful and it's history. I will always regret not being able to be there and not being able to hold my daughter's hand," he said. "My baby girl is a duchess and I love her so much. When you watch your child get married, every thought goes through your mind, every memory from the first day she was born, the first time I held her."
Thomas added, "Now I pray that Harry and Meghan can go on a nice honeymoon and rest and relax, and all of my relatives will just shut up about everything."
Here's more on Meghan's relationship with her father: