"We'll see what the situation is when we land. I do not need a photo op," Obama said en route to the country, where he will spend the three days as part of a three-nation Africa trip.
"The last thing I want to do is to be in any way obtrusive at a time when the family is concerned about Nelson Mandela's condition."
Mandela, who turns 95 next month, was rushed to hospital three weeks ago with a recurring lung disease.
His condition is said to be critical, although the presidency says there have been some signs of improvements in recent days.
Mandela's ill health means the two men, who shattered racial boundaries on either side of the Atlantic, will not hold a long-anticipated meeting for the cameras.
"I think that the message we'll want to deliver is not directly to him but to his family, is simply profound gratitude for his leadership all these years," Obama said.
Obama said he wanted to let Mandela's family know "that the thoughts and prayers of the American people are with him and his family and his country".
Reflections on Mandela's extraordinary journey from prisoner to president will permeate Obama's stay, but would not change the message of his trip.
"The lesson will be consistent because it draws on the lessons of Nelson Mandela's own life."