"But if we can, we will", Grant said.
Ms Grant reveals that the rift may have been caused when she suggested on the phone one day that her half-sister should contribute financially to the family.
Samantha, who now lives in Florida, says the last time she spoke to Meghan was in 2014.
On Christmas Day, Meghan, however, chose a stunning overcoat in a bleached shade of sand by Canadian luxury brand Sentaler, which she paired with a tan Philip Treacy hat, Chloe bag and brown suede Stuart Weitzman boots. Then a part of the hit series, Suits, Markle spoke to the magazine about her dream gown, highlighting simple styles like Carolyn Bessette Kennedy's Narciso Rodriguez slip dress as the ultimate wedding look in her book. "It's not fair that she looked that good in high school". Her last words were, 'I love you, babe. According to her, she is still hoping to be invited to Prince Harry and Markle's royal wedding but the decision is up to the princess in waiting.
Her Facebook page had nearly 800,000 likes, according to BBC Online.
A glance again at Meghan Markle's social media
Fans of the star commented on the post, with one describing her as "the ideal queen" while another wrote "now we get to see just how stunning she's going to look". "But if we can, we will".
The question of whether the President will receive an invite to the eagerly anticipated nuptials has become a contentious issue amid fears that publicly snubbing the property mogul could damage US-UK relations in the long term and hinder a post Brexit trade deal. Grant said that the alleged estrangement is far from the truth in a new interview with Fox News.
"I'd be lying to say that I wouldn't be hurt if I didn't get an invite but that's really up to her".
Meghan Markle was called out by her sister for wearing a £56,000 dress for her official engagement portrait with Prince Harry. "I can only say to Meg, "Forgive me".