Both linemen played for the Chargers in 2012 and joined the Patriots in the offseason. Both were considered potential backups for New England, which is now a little thinner on the line entering its second preseason game.
Green, 27, has made 28 career starts. The Patriots re-signed him in July after letting him go in May.
The 26-year-old Haslam started three games for San Diego in 2012.
The Patriots also confirmed they had released wide receiver Michael Jenkins, the news of which had surfaced earlier in the day.