The Giants have a bye this week before playing on the road against the 49ers (1-7) the following Monday night.
"We'll see," Shurmur said of Manning remaining the starter for that game. "But, yeah, I think Eli is our quarterback. I did say, again I know what you're all trying to tease a headline out of, at this point Eli is our quarterback and we're looking at all areas to improve. So that is where it's at."
Shurmur reiterated that the team is going to evaluate everything during the bye week when it comes to making significant changes. The Giants (1-7) are tied with the 49ers for the worst record in the NFL.
If the Giants made a switch at quarterback, it would likely be rookie Kyle Lauletta starting even though he hasn't dressed for a game this season. Lauletta is a fourth-round pick out of Richmond.
Shurmur and the Giants would have 14 days to get Lauletta ready for the 49ers if they decide to make the move. Their next two games are against San Francisco and Tampa Bay, two teams in the bottom half of the league defensively.
Lauletta has primarily been running the scout team in recent weeks. Shurmur said Monday that he has been getting some practice reps.
Manning has eight touchdown passes in eight games this season. He already has been sacked 31 times, as the Giants' offense has struggled badly to score points.
The two-time Super Bowl winner still remains optimistic he will be behind center against the 49ers. He has not been informed otherwise.
"I hope so," Manning said. "That is what the coach does. In the bye week, you evaluate everything. That is a part of his job."
Manning seems to understand that there is a draft pick waiting in the wings. He knows the possibilities with the much younger Lauletta in the quarterback room.
"I've always been a team player and do, kind of, what I'm told," Manning said of potentially needing to step aside to get Lauletta game experience. "I expect and want to be the starting quarterback until I'm told differently."
Shurmur didn't seem willing to make any decisions at this point. He's going to be part of an internal self-evaluation process this week. He said there hadn't been any demands from the front office/ownership or extensive conversations about whether to make a quarterback change.
The Giants, who began unloading players last week, are averaging 18.8 points per game. Manning, 37, has been under center for every offensive snap this season.
"Eli is our quarterback and we have to do what we can to help him be better," Shurmur said. "There is certainly a handful of plays each game where he needs to be better and I think that is pretty obvious when we all watch. So that's the approach moving forward.
"Like I said, we'll look at all things. We have a minute here to do that and I think we have to make some good decisions moving forward."
The Giants are walking a fine line. They're trying to compete on a weekly basis while not putting too much focus on the future.
"We're trying to do what we can to win this season, and certainly you always do what you can in the short run," Shurmur said. "It's hard not to look at things in the long run, but what's important is we try to put an effort on the field to beat the 49ers."
Manning: I expect to be starting QB
Giants quarterback Eli Manning talks about Coach Shurmur not committing to him as the starter after the bye week.