Vick was forced off the field with a hamstring injury late in the second quarter of the Eagles' game against the New York Giants last weekend, a match that saw Philadelphia go on to win with two fourth-quarter touchdown passes from Vick's replacement Nick Foles.
The veteran was initially expected to recover in time for Sunday's match, but Kelly has revealed that his selection would rely on how he progresses in the coming week.
"I don't know if he'll play Sunday. Right now he's day to day. We'll see how he goes through the rehab process," ESPN quotes Kelly as saying.
Meanwhile, Kelly has also insisted that the competition for the starting quarterback position is "always open".