In fact, the 32-year-old has spoken about settling down on several occasions, admitting that it would be "absolutely fantastic" to meet someone special.
Speaking to BBC while promoting the Invictus Games in Toronto in May, Harry explained that he hadn't had that many opportunities to "get out there and meet people".
"At the moment, my focus is very much on work. But if someone falls into my life, then that is absolutely fantastic," Harry said. "If or when I do find a girlfriend, I will do my utmost to ensure we get to the point where we are actually comfortable with each other before the massive invasion into her privacy."
Harry's concern over privacy is why he has strived to keep his transatlantic romance with Meghan under the radar, with the Suits actress making several low-key visits to London over the past few months so they can meet up.
But he has previously said that he would love to have someone by his side during royal tours and duties to "share the pressure", so time will tell whether the couple decide to make their relationship more public.
"There come times when you think now is the time to settle down, or now is not, whatever way it is, but I don't think you can force these things, it will happen when it's going to happen," Harry told Sky News during his tour of New Zealand in May 2015.
" Of course I would love to have kids right now but there's a process that one has to go through, and tours like this are great fun. Hopefully I'm doing all right by myself – it would be great to have someone else next to me to share the pressure, but you know, time will come and whatever happens, happens."
It appears Meghan is also keen to start a family, and the actress previously confided to HELLO! that she hoped to pass her most prized possessions on to her children one day.
"I've always coveted the Cartier French Tank watch. When I found out Suits had been picked up for our third season – which, at the time, felt like such a milestone – I totally splurged and bought the two-tone version," Meghan said.
"I had it engraved on the back, 'To M.M. From M.M.' and I plan to give it to my daughter one day. That's what makes pieces special, the connection you have to them."
The 35-year-old has also said that she believes the key to finding true love and happiness is to love yourself first. "They say happiness begins with self-love. And enjoying your own company is the very best start for that adventure," Meghan wrote on her lifestyle website, The Tig.
Meghan shares a number of glimpses into her personal life and beliefs on her website, and once said that she has no desire to stop working, especially on her humanitarian projects.
" I've never wanted to be a lady who lunches – I’ve always wanted to be a woman who works.And this type of work is what feeds my soul, and fuels my purpose," Meghan wrote.
It is a passion she shares with Harry, and the handsome Prince also has another quality that Meghan loves – a British sense of style.
"I love how British guys dress for the cold," Meghan told Esquire in 2013. "I'm from LA so I'm used to seeing people in sunglasses and flip-flops. There's something so romantic about a man in a scarf and a knitted hat."
The actress may have also been dropping hints about her budding romance with Harry on Instagram, where she has shared a number of inspiring quotes with her 1.1 million followers.
"Darling, you deserve it all. You deserve love and peace and magic and joy dancing in your eyes," one quote began. Another read: "If it's both terrifying and amazing, then you should definitely pursue it."
Fans around the world will be watching with bated breath to see where this royal romance goes!