The 26-year-old will have one final chance to stake a claim for a spot when the Patriots face the New York Giants in their last warm-up game on Thursday, with Tebow likely to play a substantial part with Brady and Mallett expected to be rested.
However, he insists that he is not even looking that far ahead as he focuses on day-to-day duties with the Patriots.
"I'm just focused on today. [It's] just another game. You focus not even on that game, but preparing for that game, focus on today, the install and having a good practice," Tebow told reporters.
"I love playing; I love competing. Everybody does in this locker room. We all love the game; that's why we're here. You just want to not focus on that, but focus on the preparation right now, and that'll take care of itself.
"I learned very early on in my career at Florida to worry about what I can control. And the things that I can't control, I'm not going to spend time worrying about. But I can control my attitude, my effort, my focus every single day, and those are things I'm going to worry about."
The Patriots' roster currently has 77 players, with that number needing to be reduced to 75 by later today and then finally 53 by Saturday.