The Pontiff has clashed with the US leader on climate change and the treatment of immigrants and refugees
So things might get awkward when the blustering American president and the soft-spoken pontiff touch base.
Here are some of the issues they have disagreed on:
Without mentioning Mr Trump by name, the Pope heavily criticised the President's promise to build a border wall and "make Mexico pay for it" in February. In remarks at the Vatican, he said it was a Christian's calling "to not raise walls but bridges, to not respond to evil with evil, to overcome evil with good”.
He continued to seemingly address Trump, saying: “A Christian can never say: ‘I’ll make you pay for that.’ Never! That is not a Christian gesture. An offence is overcome with forgiveness, by living in peace with everyone.”
The Pope's comments follow a very public spat last year. Francis seemed to criticise Mr Trump during the 2016 campaign for his positions on immigration, suggesting that his policies made the US leader “not Christian”. Mr Trump described this as "disgraceful".
The Pope started the beef while flying back to Rome from Mexico in February 2016. “A person who thinks only about building walls, wherever they may be, and not building bridges, is not Christian,” he said.
Mr Trump quickly responded at a rally, telling the crowd: “For a religious leader to question a person’s faith is disgraceful."
He added: “No leader, especially a religious leader, has the right to question another man’s religion or faith.” The now-President then accused the Mexican government of “using the pope as a pawn”.
Mr Trump also attempted to implement two travel bans early in his administration, which the Vatican called troubling.
The pope has favoured a message of inclusiveness and integration for immigration.
The refugee crisis
The president has frequently decried the wave of refugees coming out of war torn areas of the Middle East. He has said that refugee resettlement programmes could be exploited by Isis militants in their quest to commit acts of violence in the US.
During Mr Trump’s presidency, the rate of refugee resettlements have plummeted when compared with those under his predecessor Barack Obama.
The Pope, on the other hand, has encouraged acceptance when it comes to refugees, saying that you can’t defend Christianity by being “against refugees and other religions”.
His holiness has also tweeted his support for refugees, in what has been seen by many as a thinly veiled barb at Mr Trump.
I express my solidarity with migrants around the world and thank all those who help them: welcoming others means welcoming God in person!— Pope Francis (@Pontifex)December 18, 2016
How often in the Bible the Lord asks us to welcome migrants and foreigners, reminding us that we too are foreigners!— Pope Francis (@Pontifex)February 18, 2017
When it comes to climate change Mr Trump and Pope Francis couldn't be further apart.
The pope has called climate change a sin and released an encyclical - a papal document on Catholic doctrine - calling on Christians to protect the planet. Failing to do so, it says, is an immoral action that would disproportionately injure the less fortunate. When Mr Trump’s predecessor Barack Obama announced a major rule to curb greenhouse gas emissions known as the Clean Power Plan, the Pontiff cheered those efforts.
Mr Trump on the other hand openly mocked climate change while campaigning to become president. In one now-famous tweet he even said it was a hoax created by China.
Since taking office he has actively sought to dismantle the rules and regulations Mr Obama put in place.