Been announced that John Isner is playing the Atlanta Open the same week as the Olympics. On top of this we've had Dominic Thiem say the Olympics isn't a priority.
Additionally, we've got quite a few players who haven't yet qualified for the Olympics due to not playing enough Davis Cup/Fed Cup ties. Currently you need to play for your country 3 times from 2013-2016.
On the mens side, players that haven't done this:
Nadal- has only played 2 DC ties in past 4 years. Only one chance left 17-19 July. Olympic tennis starts 8th August so I think he can still qualify if he plays the DC playoffs.
Kevin Anderson- won't play the Olympics. Doesn't play Davis Cup anymore, hasn't played any ties in past years.
Benoit Paire- Also won't play (guessing). Hasn't played any Davis Cup ties ever.
Feliciano Lopez- Also don't think he'll play, has only played 1 DC tie in past years.
Jack Sock- has played 2 DC ties, needs one more to qualify. USA will play 17-19 July so has a shot i think?
Pablo Cuevas- has only played 2 DC ties, needs another to qualify. They've already lost in the playoff so don't think he can qualify but wiki has him as qualified so I might be wrong
Ivo Karlovic- doesn't play DC anymore, hasn't played DC in recent years so can't qualify
Steve Johnson- Can't qualify I don't think, has only played 1 DC tie.
Jeremy Chardy- Hasn't played any DC ties, don't think he can play
Garcia-Lopez- Only played 1 DC tie, don't think he can qualify
And those are just some of the big names
On the females side, players that haven't qualified:
Muguruza- Has only played 2 Fed Cup ties. No more ties til the Olympics though so not qualified?
Wozniacki- Only played 1 Fed Cup tie. I read somewhere she's applying to the ITF for her to qualify.
Jankovic- Only played 2 Fed Cup ties, unsure if she'll play
Kasatkina- Only played 1 tie
Gavrilova- Only played 1 tie
Feel free to add more or amend my list. Quite a few big names not playing at this point. Wonder who else won't play?!