The Mail on Sunday and its parent company, Associated Newspapers, are accused of unlawfully publishing a letter from the Duchess of Sussex to Mr Markle in February 2019.
The paper argues the publication was justified because there is a "huge and legitimate" public interest in the "personal relationships" of members of the royal family.
Legal documents reveal the Mail On Sunday will rely on evidence from Mr Markle, including that he "had a weighty right to tell his version of what had happened between himself and his daughter including the contents of the letter”.
It means should the case go to trial, both Meghan and her father could be called to testify against one another. The paper's sister publication, the Daily Mail, reported Mr Markle would be prepared to face her in court.
The duchess’s half sister, Samantha Markle, insists their father will testify in the case if asked to.
Ms Markle told the BBC: "If he is called, he will come."
What is in the letter?
Mr Markle was caught up in controversy in the build-up to Meghan’s wedding to Prince Harry in 2018 after he allegedly staged paparazzi photographs of himself and then began commenting regularly to entertainment website TMZ about his contact with his daughter.
In February 2018, the Mail On Sunday published extracts of Meghan's handwritten letter to Mr Markle.
In one extract, published by the newspaper, the duchess wrote: "Your actions have broken my heart into a million pieces – not simply because you have manufactured such unnecessary and unwarranted pain, but by making the choice to not tell the truth as you are puppeteered in this. Something I will never understand."
What is the substance of Meghan’s claim?
Law firm Schillings, representing Meghan, filed the High Court claim against the paper in October, alleging misuse of private information, infringement of copyright and breach of the Data Protection Act 2018.
When the legal action was announced in October, Harry claimed the alleged unlawful publication of the private letter was done in "an intentionally destructive manner" to "manipulate" readers.
In a statement released at the time, a spokeswoman for Schillings claimed the "intrusive" publication of the letter was part of Associated Newspapers' campaign to write "false and deliberately derogatory stories about" Meghan, "as well as her husband”.
What is the Mail on Sunday’s defence?
The paper claims the duchess "did not have a reasonable expectation of privacy that the contents of the letter were private and would remain so”.
The paper also argues the publication of the letter was in response to a "one-sided" article in People Magazine in February 2019 featuring an interview with five unnamed "close friends" of the duchess which referenced the letter, meaning its existence was in the public domain.
Documents seen by the PA news agency also argue members of the royal family "generate and rely on publicity about themselves and their lives in order to maintain the privileged positions they hold and to promote themselves”.
The Mail On Sunday said it would stand by the story and denied editing the letter to change its meaning.
‘Megxit' summit outcome
The Queen agreed Harry and Meghan could step back as senior royals and begin a "new life" as an "independent" family following a summit at Sandringham.
Buckingham Palace also confirmed the Sussexes would begin a "transition period" in which they would split their time between the UK and Canada.
It was revealed on Tuesday the duchess did not join the royal summit with the Queen and senior royals by phone and instead relied on her husband to put forward their case.
Meanwhile in Canada, the duchess was seen for just the second time since the royal crisis began, at the Downtown Eastside Women's Centre in Vancouver discussing "issues affecting women in the community", according to a photograph posted on Facebook by the shelter.