The Giants quarterback has faced Peyton Manning twice since being drafted in 2004, losing on both occasions.
The 32-year-old told the team's website: "Hopefully, when I think back on these games that we played against my brother, I can think back and remember at least one win.
"You do understand how special it is with both of us playing this game at a high level in the NFL. It is rare and we just appreciate the road we've both taken to get here and we support each other along the way. So those are special moments. Besides that, though, it's a game. You've got to go out there and try to do your job.
"It's pressure because we're 0-1 right now. We've got to get a win for this season and this team. It's the second game of this season. We've got to make improvements. We've got to get better. The mindset and the focus are just on this year and this being the second game of the season. It's a big game because of that scenario."
The Mannings are the only brothers to face each other as starting quarterbacks in the history of the NFL.