The 18-year-old only made his senior club debut in February, but eight goals in 18 appearances for Manchester United since then earned him a place in Hodgson's provisional 26-man squad for this summer's tournament.
"If Sturridge isn't fit tomorrow then I think you'll all work out [Rashford] is going to start the game. I'm happy with that, I'm more than content he can handle the situation," he told reporters.
"It doesn't take a lot of detective work to work that out, with me wanting to rest [Jamie] Vardy and [Harry] Kane. There was no doubt that my original intention was to choose between Sturridge, Rashford and possibly one other.
"With those two out, it's pretty obvious Rashford is going to play a serious part in the game."
Friday's match at the Stadium of Light is the last warm-up game before Hodgson must pick his final 23-man squad for the tournament.