Parkinson (shoulder) was listed as a limited participant on the Rams' estimated injury report Wednesday, Sarah Barshop of ESPN.com reports.
Parkinson played 53 snaps on offensive during Monday night's 37-34 overtime loss to the Bills, reeling in one of two targets for three yards. The tight end was limited at each of the team's first two practices last week before logging a full session Friday, and he appears to be potentially on track to do the same thing prior to Week 6. Parkinson will have two more opportunities to officially practice before Sunday's matchup with Arizona.