Thomas and Samantha did not attend Meghan's wedding to Prince Harry in May, and have repeatedly spoken out against the actions of the Royal Family.
Meghan has not spoken to Samantha since 2015.
Just last month, Samantha, 53, claimed Meghan had not spoken to her father since the wedding and feared she he may "die of sadness" if the pair did not start talking again.
Meghan's sister has continued to publicly slate her over her relationship with her father. Photo / Twitter
Samantha said: "I'm desperate for Meghan to meet up with Dad when she's back. If she doesn't it would be really cruel and hurtful and would break his heart."
"I speak to him every day. He's very sensitive and I see his health suffering as a result of this. I hope they can meet in a quiet place, spend some quality time together and gain closure on what's been an incredibly sad time for him.
"If they don't I'm worried he'll die of sadness. I just want her to get in touch before it's too late. Life's short – neither of them deserves to be left with the consequences."
However it does not appear as if Thomas Markle is ready to put aside his differences after he compared the Royal Family to a cult.
He said: "They are either like Scientologists or the Stepford family.
"If they hear anybody say anything they just lock the doors. They need to speak up!
"They are cult-like — like Scientology — because they are secretive.
"They close the door, pull the shades down and put their fingers in their ears so they don't have to hear."
The Duchess of Sussex has remained silent throughout the public outbursts of her family.
