"It's still sore but it's a lot better than it was yesterday," Graham told the Swans' official website.
"I've got to take each day as it comes.
"Injuries are part and parcel of the game, but I've been fairly fortunate with them so far in my career.
"I'm still hopeful of making Saturday, but I think the next 24 hours will be crucial once the swelling has gone down.
"Although it's still early in the season, Saturday's game is massive. If we can pick up a win at Ewood Park it will move us 10 points above Blackburn, which will be a good cushion to have going into the busy Christmas and New Year period.
"It's a game I want to be fit for."