Coach Pete Carroll said Sunday that Parkinson (foot) will run this week and that there's still hope he can be ready by Week 1, Brady Henderson of ESPN.com reports.
Parkinson was slated to be the third tight end behind Will Dissly and Gerald Everett this season, and still will be if he is able to return for the regular season. However, the Seahawks are likely to be extra cautious, as the 22-year-old broke the same foot last year.