Despite a strong season debut against the Philadelphia Eagles, the line remains a problem.
All starters are on the injury list before Sunday's game against the Dolphins.
Trent Brown, Sidy Sow, David Andrews, Mike Enwenu, and Cole Strange skipped Thursday practice.
The Patriots are interested in free agency offensive lineman La'el Collins due to the line's deterioration.
Running back Ezekiel Elliott is pleased that New England is interested in the former Cincinnati Bengals and Dallas Cowboys tackle.
Elliott, who played six seasons with Collins in Dallas, pushed the Patriots to sign him Thursday.