The Duchess of Sussex has been estranged from her father since her 2018 wedding.
A spokesperson for the Duchess of Sussex said: "I can confirm she has reached out to her father."
The development is understood to have only just happened.
No further details have been released, including whether or not Meghan's attempt was successful.
Meghan is said to have previously tried to reach out to him in the past.
Mr Markle, who moved from Mexico to live in the Philippines, has never met his grandchildren Prince Archie and Princess Lilibet.
The retired TV lighting director ended up in intensive care on Wednesday after a three-hour emergency surgery, the Daily Mail reported.
He was later said to have had his leg amputated below the knee after his foot turned black.
His son, Thomas Markle Jr, said before the news that the duchess had "reached out" that he hoped Meghan would show "compassion".
"My only wish is that Meghan shows my father some compassion. He is literally fighting for his life," he told the Mail.
Mr Markle pulled out of attending Harry and Meghan's wedding seven years ago after he was caught staging photographs for the paparazzi in the US, and then suffered a heart attack.
Harry's father, now the King, stepped in to walk Meghan down the aisle.
Mr Markle went on to repeatedly speak to the media and later claimed he had been "shunned" by Meghan.
He criticised the duchess but still said he wanted to reunite with her, and publicly pleaded to be able to see Archie and Lili, saying in 2023: "She is not the person I knew as my daughter."