White led South Africa to the World Cup when they beat England in the final in Paris last year but left his post in acrimonious circumstances just six weeks later.
He has since been linked with a number of posts including Wales - before the appointment of Warren Gatland - and England, when Brian Ashton's job appeared under threat.
As yet White has not secured a position - but he believes there are similarities between coaching the Lions and South Africa, with a need for someone to knit together a disparate group.
Speaking at the Laureus World Sports Awards in St Petersburg, where South Africa had just landed the Team of the Year award, White said: "It has all been hearsay, it's all been speculation.
"The Lions are going to pick a coach at the end of the Six Nations.
"I guess their concerns would be they need to get a guy who is going to blend a team together. Getting four nations to bond as one which is very similar to what we do in our country.
"We have very diverse cultures, diverse groups, language, cultural barriers - so maybe getting the Lions together is similar to getting a group of South Africans who come from different walks of life to gel as a team.
"So maybe that is why the Lions have sent sort of a message out thinking would I consider it."
The Lions manager Gerald Davies admitted earlier this month he would be open to the appointment of a foreign coach and White was drawn to a role he believes is unique in the sport.
He said: "I've never been involved against the Lions or with the Lions but it's something I've grown up with as a young South African.
"In 1974 the Lions came to South Africa and everyone still talks about that Lions team so when people ask whether you would consider it, of course I'd consider it.
"It's something in rugby that is unique, something in rugby that you get one chance to do, it's something in rugby that would probably excite me in getting back into coaching.
"I'd be very keen to be involved in the Lions because it is something that is unique to rugby union."