Presley, the only child of Elvis Presley, died on Thursday (12 January) at the age of 54 after suffering a cardiac arrest.
The Duchess of York was friends with the singer and posted a picture of the pair on Instagram, which showed them smiling with their heads together.
Read more: Lisa Marie Presley's life in photos
She said that Presley was in her heart and vowed to be there to support her family.
"I say hello to you everyday and I love you my sissy and I will continue to say hello to you everyday," wrote Ferguson, who is thought to have met Presley in 2009 whilst in the US.
"You were my sissy, an amazing mother to Ben, Riley, Harper and Finley and a superbly loving daughter to Priscilla.
"You have been my devoted friend for many years and I am here for your family to support and love them."
"I am deeply saddened my sissy, you are in my heart," she added.
Presley had four children including the actor Riley Keough, who is known for TV programmes like The Girlfriend Experience and The Terminal List.
Her son Benjamin Keough took his own life in 2020 at the age of 27.
Presley's death was confirmed by her mother Priscilla in a statement in which she paid tribute to her "beautiful daughter".
"It is with a heavy heart that I must share the devastating news that my beautiful daughter Lisa Marie has left us," she said.
"She was the most passionate, strong and loving woman I have ever known.
"We ask for privacy as we try to deal with this profound loss.
"Thank you for the love and prayers.
"At this time there will be no further comment."
Watch: Pink, Octavia Spencer and more pay tribute to Lisa Marie Presley