Vick is out with a concussion and Reid said on Monday that Vick had still not recovered from the injury.
Reid says he talked with Vick about the demotion but said the decision to start Nick Foles was his.
Reid went on to say Vick would most likely be second string when he gets healthy, saying he wants Vick to have a long career here.
Earlier in the day, the Eagles announced the firing of defensive line coach Jim Washburn.
Taking Washburn's place will be Tommy Brasher, who previously served as the Eagles defensive line coach in 1985 and again from 1999-2005.
In a statement released by the Eagles Monday morning, head coach Andy Reid is quoted as saying, "Jim is a fine football coach and we appreciate the efforts he gave to this team over the past two years… However, I determined that it was in the team's best interest that we move in a different direction in terms of trying to maximize the production of that position group. We look forward to having Tommy Brasher back on board to work with the defensive line."
The Eagles hired Washburn before last season, expecting his wide-nine defensive line alignment to produce plenty of pressure on opposing quarterbacks. The scheme helped the Eagles tie for the league lead with 50 sacks last season but has resulted in only 20 so far this year.
Washburn's firing comes a day after the Eagles dropped to 3-9 with a 38-33 loss to Dallas in which Tony Romo finished 22 for 27 for 303 yards and three touchdowns.
Last week, the Eagles released defensive end Jason Babin, who excelled in Washburn's scheme while in Tennessee.
Information provided by The Associated Press was used in this article.