The Rugby Football Union have said there will be no knee-jerk reaction to England's failure to get through the pool stage at a World Cup for the first time but Lancaster's position will be reviewed after the final match against Uruguay next weekend.
White, who led South Africa to their second World Cup triumph in 2007, has been touted as a candidate to become England's first foreign coach along with the likes of Japan coach Eddie Jones and New Zealand assistant Wayne Smith.
"England have everything going for them in terms of resources, players and history," the 52-year-old, who is currently at French club Montpellier, told the Daily Mail.
"If they were genuinely interested and they approached me, of course I would be interested. It's one of the biggest jobs in world sport and you'd be crazy not to consider it."
Mike Ford, one of the leading English candidates for the job, should it become vacant, ruled himself out of the race on Tuesday.
"I have just signed a four-year contract with Bath Rugby and my only intention is to help them realise their full potential," he wrote in the Daily Telegraph.
White was convinced that England needed a coach with experience of leading teams in test rugby.
"Since 2003, England have been going backwards," said White. "For a big rugby nation like England to be eighth in the world isn't right.
"International rugby shouldn't be a learning curve for coaches. It's a business now. The last three World Cups must send a message; if you go for a coach who's never coached international rugby, it's going to be same old, same old.
"They've tried it with Andy Robinson, Martin Johnson and Stuart Lancaster. They have one of the biggest budgets in the world but their coaches only have a few years' experience."
Jones, a former Australia coach and technical assistant to White with the Springboks in 2007, has also said he would listen to an approach from the RFU.
White, however, said he felt he had been somewhat used by the RFU during the selection processes for the post of Professional Rugby Director and the last two head coaching appointments.
"When I was with the Boks, I was approached to put my name in for Rob Andrew's job. Then they contacted me before appointing Martin Johnson and Stuart Lancaster," he recalled.
"All three times, they've gone for English people. Generally it's used as a means to make the other candidates look like they have a bit of credence."
(Reporting by Nick Mulvenney, editing by Sudipto Ganguly)
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