Griffin suffered a serious injury to his LCL and ACL last season, ultimately requiring surgery that has kept him out of action for seven months.
However, Shanahan is pleased with the progress that the 23-year-old has made in his rehabilitation and plans to move to a second stage of training following their pre-season match against Tennessee Titans on Thursday.
"I thought he had a good week. The best part about it, there wasn't any setback. As you have a plan going into your first week, you're hoping you can execute that game plan. We were able to do that," Shanahan told The Washington Post.
"After the game [on Thursday], we've got a little bit different game plan. If there's no setback, I'll share that with you next week when we implement it.
"The reason why I don't tell you at the beginning, if there is a setback, I'm not going to tell you, anyhow."
Griffin won the 2012 NFL Offensive Rookie of the Year last season.