The Vatican has said the meeting between the pontiff and the former Cuban leader is "highly likely" to take place in the capital, Havana.
According to The Times the Pope will then visit two other Cuban cities, Holguin and Santiago de Cuba.
Fidel Castro, 89, supressed the reach of the Catholic Church after he took to power in 1959.
Mr Castro was then excommunicated from it by Pope John XXIII, who later reduced the restrictions.
He then met Pope John Paul II and Benedict XVI in 1998 and 2012 respectively.
Pope Francis is also expected to visit Castro's brother, Raul, the current country leader.
He praised the Pope for helping ease conflict between Cuba and the USA.
After visiting the Vatican, President Castro said: "I read all the speeches of the Pope, his commentaries, and if the Pope continues this way, I will go back to praying and go back to the church, and I'm not joking."
The Pope continues his trip by visiting the United States for a six day tour.
There are fears that the Pope's Cuba visit could anger US conservatives though.
He is expected to visit Ground Zero in New York city, as well as President Obama and will hold a rally in Philadelphia where Aretha Franklin will perform.
