During his trip, the US president will visit Robben Island, where Mandela was imprisoned for 18 years. He will also meet Archbishop Desmond Tutu and speak at the University of Cape Town.
"The last thing I want to do is to be in any way obtrusive at a time when the family is concerned with Nelson Mandela's condition," Obama said.
Obama has called Mandela a "personal hero" and said the imprisoned activist's willingness to risk his life for the cause of equal rights helped inspire his own political activism. Obama said his message during the visit will draw on the lessons of Mandela's life, with a message that "Africa's rise will continue" if its people are unified instead of divided by race or religion.
"I think the main message we'll want to deliver if not directly to him but to his family is simply a profound gratitude for his leadership all these years and that the thoughts and prayers of the American people are with him and his family and his country," Obama said.
The White House later confirmed that he and Michelle Obama will "meet privately with members of the Mandela family to offer their thoughts and prayers at this difficult time".
Obama met Mandela in 2005 when he was still a US senator. Both men became the first black presidents of their nations and have received the Nobel Peace Prize. His wife and daughters had a private meeting with Mandela in 2011.
The US President has described Mandela as a "hero for the world", whose "legacy will linger on through the ages".
Obama will finish his Africa tour in Tanzania. It is his first prolonged trip to the continent since he was elected president in 2009.
