Does the camera pan, zoom, tilt, or move at all?
This will be exponentially harder if it moves.
Basically, you will have to get a layer with a clean image of the field, rotoscope out your single player on another layer, and have the full play on a third layer.
What you describe is Effects --> Keying --> Difference Matte. Though due to technical things like compression artifacts and naturally potential overlaps with other players you may still face quite some manual work with mask and all that. And as Szalam already said - the more motion, the more difficult it will be.
Depending on the shot you could do a lose roto around most of the players on the field and then use copies of the footage offset in time to fill the holes. Let me explain a bit more. Think of only two players on the field. Player A, the one you want to keep, and Player B, the one that you want to remove. As player B moves from left to right you animate a subtraction mask around the player which cuts a hole in the shot. Player B is now gone but so is the playing field. Half of your job is now done. All that is left to do is fill the hole with the playing field. If the shot is a locked down shot then all you have to do take a copy of your footage and put it below the footage with the hole and shift the footage on the bottom back or forward in time so that Player B does not appear in the holes. Did you follow that? It's pretty simple really, Player B only crosses the 40 yard line between frame 200 and frame 220 so if the bottom layer is shifted 20 frames ahead then the 40 yard line will be there to fill the hole as it passes.
If you have a hand held shot or a moving shot you can still use this technique, you just have to do some motion tracking so the position of the bottom layer can be adjusted to fill the hole properly.
If you have a bunch of money in the budget there is an automated way to do this with software. Mocha Pro is one option. There are others.
The hardest part of this kind of a project is where one of the other players occludes or passes in front of Player A. This will require some real fancy and careful time resampling to find parts of Player A that you can use to fill the hole created by Player B's mask.