If the 23-year-old fails to recover in time, her absence would be a massive blow for the reigning champions.
"She's still recovering," England coach Sarina Wiegman said on Friday. "She's doing things on the pitch and we have two more days so we're going to give her time. Don't know yet (if she'll be ready), but that's what we're going to go for – 23 players available for the game on Sunday."
James has nine goals in 33 appearances for England, including two in their 4-0 victory over the Netherlands in the group stage in Switzerland.
"You give LJ the ball and you know she's going to run through everybody and try to get her shot off," teammate Georgia Stanway said earlier in the tournament.
James injured her ankle just before halftime on Tuesday and watched the second half from the bench with an ice pack on her ankle.