The song has taken a 30% lead over its nearest rival, George Ezra's Shotgun, the Official Charts Company said.
Originally recorded for the Euro '96 tournament, Three Lions was written by The Lightning Seeds and comedians Frank Skinner and David Baddiel.
Its famous "football's coming home" chant has been resurrected as England have progressed through the World Cup.
The song re-entered the top 40 last Friday, but its popularity surged further after England beat Sweden on Saturday to reach the semi-finals.
In the 24 hours after that match, Three Lions topped the iTunes download chart and was streamed 701,000 times on Spotify alone.
In total, it has accumulated 24,000 downloads and 2.6 million audio streams since last Friday.
That combination is enough to put the song in pole position in the midweek chart update, with two other football anthems also on course to reappear in the top 40 - Fat Les's Vindaloo at 28 and New Order's World In Motion at 34.
"Thanks to you lovely people, Shotgun has been number one for two weeks running," he said. "Of course that is amazing. But I think it's time we knock it off the number one spot with Three Lions."
Chart analyst James Masterton told the BBC: "The British people have a proud history of sending songs flying up the charts in spontaneous outpourings of joy.
"Witness the way Ant and Dec ended up at the top of the charts five years ago after doing Let's Get Ready To Rhumble on TV.
"It seems only right that we've rediscovered a love of Three Lions at the same moment we are all rallying behind the England team. Music and football are the two things which unite us all, it appears."
Writing in The Sun, David Baddiel said the song's lyrics had been reframed by England's unexpected success in Russia.
"When we wrote the song, the refrain 'football's coming home' referred both to the fact the tournament was being held in England, and to the more mystical idea that we might win.
"But now the song seems to mean only 'we might win', and as [last] week went on, and the jubilation rose, 'Yes, we are going to win'."
Three Lions' achievement is particularly notable because current chart rules penalise songs that are more than three years old.
Whereas every 100 streams of George Ezra's Shotgun count as one "sale" in the official chart formula, the ratio for Three Lions is 200:1.
If the streams are on an ad-funded service like YouTube or Spotify's free tier, the ratios are even more unfavourable - 600:1 for new songs vs 1,200:1 for older ones.
The rule is partly designed to keep the charts moving, especially at Christmas, when festive songs can clutter up the top 40.
It also inoculates the chart against campaigns like the one to get Ding Dong! The Witch Is Dead to number one when Margaret Thatcher died.
By coincidence, this week's chart sees a similar attempt, with protestors hoping to get Green Day's American Idiot to number one to coincide with President Trump's visit to the UK.
In the midweek chart update, the song appears at number 18, but is likely to fall by the time the final chart is revealed on BBC Radio 1 this Friday.