This app was mentioned in 11 comments, with an average of 1.55 upvotes
I've spent an obscene amount of time playing Pro Football Coach on Android (https://play.google.com/store/apps/details?id=com.achijones.profootballcoach&hl=en). There's a college football version too, if that's more your thing.
There actually is a simple pro football android app: https://play.google.com/store/apps/details?id=com.achijones.profootballcoach
But all current development is focused on college football. Main reason is that I think there are more NFL-style games available; college football has far fewer quality games IMO.
Its a pretty fun football sim. You pretty much act as the gm/owner by drafting and signing various players. Its actually pretty fun. Make sure to get the nfl 2017 roster off this subreddit.
https://play.google.com/store/apps/details?id=com.achijones.profootballcoach
This one isn't super in-depth, and admittedly RNG takes a very big role in the game, but if you're just looking to manage salary, mess around with trades, and draft high potential rookies, it's not a bad option for mobile. https://play.google.com/store/apps/details?id=com.achijones.profootballcoach&hl=en
Oh, one more thing. If you want the actual team names and a roster that is sort of based on reality, you need to download a roster. As far as I know, this is the most updated one: https://www.reddit.com/r/FootballCoach/comments/d2jsg5/pro_football_coach_2019_nfl_roster/
https://play.google.com/store/apps/details?id=com.achijones.profootballcoach&hl=en
Its worth the $1, even if you get tired of it after 5 hours.
I downloaded it last night at 9pm, and was up until 2 am in bed playing.
It's all non NFL stuff (licensing) but you can download the NFL2016 roster, which is linked in the game.
It's a football simulator! It's like madden except you can't play the games. It's a very good numbers approach to the game of football.
https://play.google.com/store/apps/details?id=com.achijones.profootballcoach&hl=en
there's also one for college. And the seasons go by quick so it takes up as much time as you want it to
It’s Android only, https://play.google.com/store/apps/details?id=com.achijones.profootballcoach
Madden franchise if you need it flashy
https://play.google.com/store/apps/details?id=com.achijones.profootballcoach
Also their is a college variant made by the same DEV
https://play.google.com/store/apps/details?id=com.achijones.profootballcoach&hl=en just found out Pro Football Coach has been released, but only for Android