However the two private equity groups are likely to face bidding competition from their US rival Carlyle, according to the Financial Times.
The newspaper added that people familiar with the auction believe Permira an Axa are favourites.
Before joining forces to bid for Opodo, Permira and Axa had been competing head-to-head to acquire mid-sized European internet travel agencies.
Last year Axa outbid Permira to buy Go Voyages. Conversely Permira beat Axa in the fight to buy the Barcelona-based online travel group eDreams.
But after teaming up, the two groups reportedly plan to buy Opodo, which is being sold by Amadeus IT Holding, and combine it with eDreams and Go Voyages to create a European travel behemoth.
Opodo accounts for just four per cent of Amadeus’ total revenue.