The 29-year-old picked up a thigh strain following the third Test at Edgbaston.
Anderson took part in fielding drills yesterday but he did not bowl in the afternoon.
“I honestly didn't know he was injured until this morning when he told me everyone was saying he's not going to play," Swann told reporters.
“Jimmy seemed fine to me - I'm sure it's just a bit of stiffness. He didn't seem to be limping from the car.
“I'm sure once he gets running around, he'll want to play. I know how well he's bowling at the minute, and when he's doing well he's hungry for the ball and just wants to keep going.”