The fact that your nephew can control his talking when the reward is appealing enough to him suggests that a positive approach will work. The key will be to find rewards for which he is willing to consistently work.
Your nephew's parents should ask the teacher to send home a daily note (could be as simple as a check mark or a smiley face) to let them know how his day went. Many eight-year-olds (and your nephew may be one) need more immediate feedback on a daily basis instead of waiting until the end of the week. He is also old enough to help determine the rewards and consequences for his behavior; his parents can sit down with him and ask for what he is willing to work, as well as what consequences would be effective with him.
The key to any system like this is to enforce both the rewards and consequences consistently over a long period of time. Rewards don't have to cost money; a good day can earn extra computer time or a walk around the block with his parents; three good days in a week can earn having a friend over to play on the weekend. Appropriate consequences would be that he would not get computer time or have a friend over to play.
Your nephew's parents may also want to talk with the school counselor. She may be able to give your nephew some individual time or include him in a small group on good behavior.