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Owen Smith has been campaigning for his Labour leadership bid for the past week.
The result of the election, decided by Labour members, will be announced on September 24 - just before the party conference.
Corbyn is still the favourite but his odds are slipping, while Owen Smith's continue to improve after a week of campaigning.
Smith formally announced his leadership bid on Sunday at the College of the Valleys in south Wales, and has made tackling inequality a major part of his vision, saying:
"We need more than posturing, we need more than sloganising. It's not enough just to be anti-austerity, you have to be pro something. I'm pro-prosperity, I am pro standing up for working people."
Voting on the next Labour leader has been a source of great controversy. The National Executive Committee's (NEC) decided last week that Corbyn would automatically be on the ballot without needing votes from his own MPs - many of whom have openly rebelled against him in a vote of No Confidence.
The decision provoked Labour party donor Michael Foster to say he will launch a legal action the NEC, but constitutional expert Dr. Peter Catterall told Business Insider that it was a "waste of time" and would only make the party's infighting even worse.
The NEC has also decided that Labour members who joined after January 12 must pay a £25 fee to vote for the next leader. While it is unclear what impact that will have on Corbyn, bookmakers seem to think the whole situation is increasingly good for Smith - though it seems Angela Eagle now has no chance at the leadership.
Here are the odds for the Labour leadership election from the main bookmakers
- Ladbrokes: Corbyn 8/13 - Smith 11/8 - Eagle 16/1
- Coral: Corbyn 8/13 - Smith 11/8 - Eagle 12/1
- Betfair: Corbyn 4/6 - Smith 10/11 - Eagle 16/1
- Paddy Power: Corbyn 8/13 - Smith 11/8 - Eagle 12/1
- Sky Bet: Corbyn 5/6 - Smith 1/1 - Eagle 18/1