At today's IOC Press Commission meeting in the Olympic capital, Lausanne, Bach spoke of his meeting with the iconic South African revered around the world.
"When I met him in South Africa we had a nice, interesting and in-depth conversation. I asked him: 'After so many years in jail, don't you feel hunger and hate?'
Mandela answered: "Not at all".
"He saw the doubt in my eyes and continued: 'If I would hate I would not be a free man'.
More From This Section
The IOC flag is being flown at half mast in honour of Mandela.
Madiba, as Mandela was fondly known, had been battling health issues in recent months, including a recurring lung infection that led to numerous hospitalisations.
Mandela, who emerged from prison after 27 years to lead South Africa out of decades of apartheid before becoming the country's first black leader, had faced several health scares over the years.
His most recent hospital stay spanning over three months was his longest since he walked free in 1990.
Other sportspersons worldwide have also mourned the death of Mandela.