The meeting is thought to be taking place later this month when the Duchess is planning a solo visit to the US.
A source told The Mirror Mr Markle is “keeping two dates free at the end of the month”.
He is reportedly “delighted” his daughter has agreed to meet.
The source claimed: “The possibility of a reunion has been discussed and Meghan looks set to incorporate it into her trip.
“The location and exact dates will be top secret for both their sakes.
“It is a very sensitive time for them, but the intent seems to be to heal the rift.”
The meeting is expected to take place in Los Angeles, meaning Mr Markle would need to travel from his home in Mexico.
It’s believed the pair have only communicated by text since Meghan married Prince Harry in Windsor on May 19.
Mr Markle, aged 74, was due to walk his daughter down the isle during the wedding but pulled out due to health surgery.
Meghan was instead accompanied by Prince Charles as she walked through the church.
Before the wedding Mr Markle caused controversy when it was revealed he had been paid to stage photographs with the paparazzi.
At the end of last month Mr Markle gave an interview to the Mail on Sunday in which he claimed Princess Diana would have “loathed” the way the Royal Family is treating him.
He also accused Meghan of having a “sense of superiority” and said she had changed her phone number, so he has “no way of connecting with my daughter”.
During an earlier interview with Good Morning Britain Mr Markle broke protocol by saying that during a conversation with Prince Harry about President Trump he was urged by his son-in-law to “give him a chance”.
He also told presenters Piers Morgan and Susanna Reid he was “very proud” watching his daughter getting married.
Upset by his inability to attend, he added: “The unfortunate thing is I am now a footnote in one of the greatest moments in history rather than the Dad walking her down the aisle.”