Both players were knocking the ball about freely Tuesday after missing the previous day's session in the wake of the 1-1 draw with Group C rival United States.
Rooney got a kick to the ankle Saturday, while Cole usually takes an extra day's rest after matches.
Center back Ledley King, whose groin injury is being assessed by medics on a daily basis, missed training as expected.
"It will be a blow if Ledley is out. We've got good replacements, but Ledley is a big, big player for us," England striker Peter Crouch said. "We hope he will recover as quickly as possible."
Crouch also hopes the team can recover from the setback of the opening draw with the United States.
"We haven't lost the game, like a lot of people have made out, and we will go into the next game full of confidence and do better," Crouch said. "It's not all doom and gloom. We have two more games to come and we have to make sure we get it right and go through."