Let's start by getting this out of the way: NFL teams do not really "tank," especially not in the hopes of landing one specific college prospect.
The Dolphins did not really "Tank for Tua" last year, though they may end up drafting Alabama quarterback Tua Tagovailoa anyway. Instead of losing on purpose, they tried their hardest all year and actually ended up out of position to draft LSU's Joe Burrow, the top quarterback in this year's class. And while some Browns fans keep retconning the team's 1-31 record in 2016-17 into what they hope will eventually be a triumphant narrative (Tank Wars Episode IX: The Rise of Moneyballer), what the organization really proved three years ago was that too much talk of tanking will get everyone fired.
So "Tank for Trevor" is more of a fun headline/rallying cry than a reality. With that said, some teams look like they are going to stink this year, and Clemson quarterback Trevor Lawrence is currently the best quarterback prospect in the class of 2021. So if some team just happens to spend 2020 eating cap space and noodling at quarterback and then accidentally ends up in position to select a guy who has already led his team to two national championship games, all's well that ends well, right?
Let's look at some teams that have positioned themselves to be in market for Lawrence or some other top quarterback prospect in 2021. We'll start with some teams that probably couldn't tank if they tried. Then we'll get to a pair of teams so good at losing that they could find themselves at the top of the 2021 draft board.
New England Patriots
Signs they are tanking
The current quarterback depth chart starts with Jarrett Stidham and Brian Hoyer, a fine tandem if all you hope to win is a fourth preseason game or a Music City Bowl. The skill position corps is still mostly populated by the guys who made Tom Brady look old last year.
Signs they are not tanking
Suggest "tanking" to Bill Belichick and he will glare at you until your skull melts. But beyond that, the Patriots retained veterans such as defensive backs Jason and Devin McCourty, guard Joe Thuney and special teams ace Matthew Slater. A team planning to bottom out and start over would likely shed many of those salaries.