The team name and logo would not be used. Team color would be used for the background. The font would not be specific to the team.
This smacks of both trademark infringement as well as a violation of those players right to publicity and privacy.
The NFL has rights not only in their specific trademarks (text and logos) but also in their "trade dress" (see link below for more detailed explanation of this). This means that merely using their colors on a jersey would be a infringement without their permission. Adding a player's name from that team and you have nailed in the coffin lid.
Please consult a lawyer for some specific guidance before you jump in here.
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Contracts / Agreements Lawyer
I agree that there may be a serious trademark issue here. It would be possible to go other directions with that idea if you're so inclined though.
Intellectual Property Law Attorney
I agree. The short answer is that there would likely be both trademark infringement as well as a violation of those players' right to publicity and privacy.
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