Negotiations are being finalised and Titan has been named as preferred bidder, with a contract due to be signed imminently.
Previously thought to be worth £4m a year, the contract is now expected to total £50m over a five-year term.
The growth in revenue will come from an expansion in the advertising estate at Asda. The new contract allows for advertising to be introduced for the first time at the group's 19 supercentres, and to a further 60 large stores.