White had been disappointed with SA Rugby's decision to advertise his position following the World Cup success, prompting him not to re-apply for the post.
And after admitting he had "taken a step back from the game" following his final match in charge of the Springboks against the Barbarians at Twickenham on December 1, White indicated he was keen to make a return to coaching.
When asked about the possibility of leading the Lions on their tour of South Africa, White told Sky Sports News: "The Lions is something that excites me. As a young boy in 1974 the Lions came to South Africa and they smashed South Africa and it's something that is very clear in my mind.
"If there is an opportunity to coach the Lions then who knows? One day I would love to coach the Lions.
"Never say never."
Having added a World Cup medal to his list of honours - which includes a Tri-Nations triumph, an Under-21s World Cup and twice being named IRB International Coach of the Year - White admitted he needed to take a break from rugby.
"I got to a point in my career where I had to take a step back from the game," he said.
"The laws of the game are changing and the game is developing in different ways. I got to a point where I needed to take a step back and ask myself what excites me about rugby.
"If the right job comes along and it's one I think I can add value to then of course I'll be back."