The couple is set to marry in either Reno or Las Vegas after two years of dating.
Mr Markle Jr told DailyMailTV: "Starting out the New Year by bringing our family closer together is definitely on the to-do list - it's very important".
The news comes just days after Meghan's father, Thomas Snr., begged her to contact him in another press interview.More news: Investigation launched into alleged abuse received by Simon Zebo
The socialite explained, "Everything I hear is that Harry is completely beguiled by Meghan and completely enthralled to her and has changed considerably". "I would like to thank everyone who has offered generous messages of support".
Thomas has since made controversial statements about his daughter and has admitted that he lied to Harry about staging paparazzi photos as the couple was preparing for their special day.
British tabloids also cited an unnamed Suits actor who said: "This is all supposed to be hush, hush but it's a bit of an open secret that they'd do anything to get her and Patrick back as guest stars".More news: China envisions moon base after far-side success
Meghan became quite close with her co-stars during her seven years of filming, with many of her cast members attending the royal wedding.
Whether it's a well-fitted black dress or a shared love of striped shirts, here are all the times Meghan tipped her Philip Treacy hat to Princess Grace's iconic style.
Speaking of moving past things, a royal insider also spoke to ELLE about the rumored feud between Meghan and her sister-in-law Kate Middleton, saying, while the two may not be BFFs, they are by no means enemies.
"She's a very protective, down-to-earth person who won't be fazed by anyone's status - even the Queen's. How can I help you?'"More news: China's Lunar Rover May Face Challenges On Moon's Far Side