The Kiwi was part of the staff for the last series against the Boks in 2009 and has since been the head coach of both the 2013 win in Australia and this summer's draw in New Zealand.
With his Wales contract set to expire after the 2019 World Cup, he is widely expected to return to his homeland, either to coach domestically or to retire.
Gatland was subjected to mountains of abuse from the press during this summer's tour and immediately insisted he would not be putting himself forward for the role in South Africa.
However, having had time to think the situation over, the 54-year-old has now suggested he could give it another go if things go well over the next few years.
He told Sky Sports: "At the time when I reflected, there was some gloss taken off the experience of the Lions and potentially there was a chance for someone else to take over the mantel in three or four years.
"But you reflect back on things and after 2019 when Wales have won the World Cup, if someone said to me 'would you consider your position?' then you might think about that."