White led the Springboks to glory in Paris last month and, though Brian Ashton defied the odds to guide England to the final, his position has been subject to speculation.
White's agent Craig Livingstone told the Sunday Times: "They (England) have been in touch.
"England are busy with the (post-World Cup) review process and then they will make a decision.
"We have expressed an interest and so have they. We've been talking to Rob Andrew (Rugby Football Union director of elite rugby)."