Manuel's injury, which occurred on a third-quarter scramble in the Bills' 37-24 loss to the Cleveland Browns on Thursday night, will not require surgery.
"It's early on now to really give an exact time frame or even a window. What we need right now is for it to calm down and see where it's at," Marrone said. "Probably in a week see how it's progressing, see where he is, then get it down into a little bit more of a window."
The Bills will add a quarterback to their roster who could start when Buffalo next plays, on Oct. 13 against the Cincinnati Bengals.
"We will be looking to bring in another quarterback. We're in the process of that right now," Marrone said. "It's not a stretch [that the new quarterback starts against Cincinnati]. I think it all depends on who it is, what we get, what their background is in their system."
Marrone said the Bills could start undrafted rookie Jeff Tuel, who replaced Manuel on Thursday night and is the only healthy quarterback on the roster.
"I would say it's possible," Marrone said, "only because we're going through the process right now. By the end of the weekend, I'll have a lot better feel for what we're trying to accomplish, seeing who we're going to bring in."
After he was defensive following Thursday's game about Manuel's decision to try to gain extra yardage on the run, Marrone softened his tone Friday.
"We tell them to be smart. We tell them to slide. We tell them to get the first down and get out of bounds," Marrone said. "I don't want to make it [seem like] we're telling them never to slide, never to go down or put yourself at risk. But it's very difficult to coach the competitiveness out of a player."
Browns safety Tashaun Gipson, who made the hit, said Manuel wasn't trying to get out of bounds, but Marrone saw the play differently.
"This one last night was a tough situation, because I don't think he saw the guy coming until late," Marrone said. "But you can see him looking to get out at the point. You see him get the first down, try to get as much as he can and then try to protect himself."