The Sun says the Gunners winger is set to miss three months after dislocating a shoulder in training ahead of England's win over Germany on Wednesday.
Walcott, 19, earns £30,000 a week - and Arsenal will claim for each of the 12 weeks he is out.
Premier League clubs are entitled to up to £1.1million to cover a player's wages under the FA's insurance plan.
Gunners boss Arsene Wenger said: "There should be compensation. It's a bit of a blow as he's just taking off and it's an important time. I don't know the circumstances of the injury but accidents happen."