England 2018 Ltd, the company responsible for the country's bid to host the global extravaganza, is believed to be seriously considering the possibility of using the 82,000 capacity venue, although the Rugby Football Union (RFU) have yet to be contacted about any proposal.
The second-largest stadium in the country, behind 90,000 capacity Wembley Stadium, is seen as an ideal facility to stage several matches of the tournament, due to its extensive corporate and media facilities.
However, the RFU may not be easily persuaded to allow football to be played at the arena - as it has been used solely as a rugby venue since 1909 - although the financial rewards of hosting up to three World Cup matches would be considerable.
Despite the train system around the ground proving to be seriously problematic for fans after matches in the past, Twickenham is close to motorways and Heathrow airport.
FIFA have indicated that any one city can have up to three stadiums to stage games, with Wembley and Arsenal's Emirates Stadium likely to be selected.
“Approximately 12 stadiums, with minimum capacities of between 40,000 for group matches and 80,000 for the opening match and final, are required to host the FIFA World Cup," said Jerome Valcke, FIFA Secretary General in the Bid Regristration document sent out to all 11 prosepective bidders of the 2018.
"In addition, the very highest standards of TV broadcasting, information and telecommunications technology, transport and communication are a must.”
Manchester will almost certainly stage games should England host the World Cup, with both Old Trafford and Eastlands suitable venues, while Liverpool would hope to have a new arena in Stanley Park built by 2018.
The North-East of the country could provide at least two stadiums from Newcastle's St James' Park, Sunderland's Stadium of Light and the KC Stadium in Hull.
While Aston Villa's home, Villa Park would be an almost certain representitive from the Midlands.
