BA has shortlisted incumbent M&C Saatchi along with JWT, DDB London and Bartle Bogle Hegarty.
Bookmaker Paddy Power said M&C Saatchi is still hot favourite with only a slight narrowing in odds. Earlier this month, the Irish bookmaker was offering odds of 8/11 for the agency to win the account, which have now revised to 1/2.
The second favourite at 3/1 is BBH, followed by DDB at 5/1 and JWT as the 8/1 outsider.
A spokesman for Paddy Power said: "We are expecting it [M&C Saatchi] to retain it this time around. However, the BA market has taken off since we opened it and BBH supporters have been particularly bullish about their chances."
The next round of pitch meetings are scheduled for September and will be overseen by head of global marketing Jill McDonald and head of marketing UK and Ireland Jayne O'Brien.
The Saatchi brothers have held the account for 20 years, with M&C Saatchi holding it for 10 years. Losing the account would be a devastating blow to the agency, because it represented around 6% of its 2004 revenue.
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