The 48-year-old's position with Australian Super 15 side the Brumbies was expected to rule him out of the running for the role with the Rugby Football Union, especially as White is only in the early stages of a four-year deal in Canberra.
But while White has reaffirmed his commitment to the Brumbies, his comments in a BBC Radio interview suggested he would welcome an approach from Twickenham.
"During the World Cup there were times when I thought it would be wonderful to be back on this stage," White told 5 Live's Sportsweek programme.
"I'm sure that if an opportunity came about, it's something I'd like to do again.
"I don't know how I'd react if I was called [by the RFU], one never knows until you are in that situation.
"All coaches want to test themselves against the best and when you've won one World Cup, you'd like to win a second.
"It would be a fantastic achievement to become the first coach to win two World Cups. It would be a dream come true.
"England have to get a winner, someone who's been there and done it, someone who understands what it takes to win something special.
"They must get back to where they were when they were the dominant force in rugby. They do that by getting someone who the players respect for having been there and done it.
"England are a sleeping giant. Whoever gets that job right can have a very successful time with a very powerful rugby nation."
White also made it clear that he would be open to working alongside previous World Cup winning coach Sir Clive Woodward after admitting that the pair have already discussed possible coaching partnerships.
Woodward is currently employed by the British Olympic Association and has committed himself to that organisation until after the 2012 games but that hasn't stopped calls for him to be reappointed as elite rugby director by the RFU as soon as possible.
And with Saxons boss Stuart Lancaster being tipped to coach the senior side in a caretaker role in next year's RBS 6 Nations, the prospect of a White-Woodward double act is likely to receive plenty of headlines over the coming weeks and months.
"I've chatted to Clive about coaching together," added White.
"He's a very proud man who's been through the highs and lows with England and took them to the World Cup.
"I say this not because Clive is my friend, but it's amazing how a guy like him hasn't stayed in rugby when he's achieved the ultimate in winning the World Cup with England."