The two men are expected to discuss cancer research and cures.
Speaking on Friday Mr Biden, who is a Catholic, said he had plans to connect medical research with issues surrounding societal and moral issues that Pope Francis has spoken about in the past.
During his visit to the Vatican the pair are expected to discuss how the medical and faith community have not always seen eye-to-eye.
Joe Biden has often said he wants faith and science to work more closely together, according to The Washington Post.
In 2015 he lost a son, Beau (pictured) to brain cancer.
Since then Joe Biden announced he would not run for president and instead launched a special task force with President Barack Obama asking US Congress for $1 billion (roughly £700 million) over two years for specialist cancer research.
Only a small proportion of it has been approved so far.
Speaking in March to the American Association for Cancer Research, Mr Biden said he had noticed how leaders from all over the world wanted to speak to him about cancer.
He said: "I believe together we can redesign a new system - or adjust to a new system - that better supports your efforts and saves lives sooner than otherwise.
"Because I really do believe we're on the cusp of breakthroughs that will save lives, benefit all of humanity."