Bookmaker Coral has slashed the odds on the 1996 hit reaching number one from 10-1 to 3-1.
If the song reaches the top, it will be the third time it has seen such success after 1996 and 1998.
Coral's Harry Aitkenhead said that the inclusion of streaming numbers could boost the track's chance of seeing number one once more.
"England have started the World Cup brilliantly and every pub and club up and down the country is playing the Baddiel and Skinner classic," he said.
"If football really does come home you can be sure that Three Lions will be roaring towards number one, and we think it's got a real chance of hitting top spot.
"The fact that the charts are changing to include streaming sites such as YouTube is also a massive boost for a potential run to UK Number One, with people sure to be blasting it out ahead of any big games."
The song was re-recorded in 1998 and a new version was brought out in 2010 featuring Robbie Williams and Russell Brand.
To date, the song has sold 1.6 million copies.
At 3-1, the odds for the song are higher than Coral's prediction for England winning the World Cup, currently at 9-1.