Add the Miami Dolphins to the list.
According to ProFootballTalk's Mike Florio, the Dolphins "covet" Burrow.
"Specifically, the guy who signs the checks—owner Stephen Ross—is the one who wants Burrow," Florio added. "It's unknown at this point whether coach Brian Flores and/or GM Chris Grier agree."
Miami owns the No. 5 overall pick after finishing 2019 at 5-11.
Burrow is expected to go first overall, which would place him with the Cincinnati Bengals if they decide to stay at No. 1.
ESPN's Adam Schefter reported Sunday that the Bengals "have no intention of trading" down, but Cincinnati director of player personnel Duke Tobin hit the pause button on that.
"That's news to me," Tobin said Monday in response to Schefter's report, according to team reporter Geoff Hobson.
Tobin continued: "I don't know that any decision has been made for what we're going to do in April. We're early in the process. We certainly haven't had any meetings to determine that at this point. Those will be meetings we'll have as we go through the process."
If the Bengals are open to trading away their top pick, Miami has the most enticing assets to offer Cincinnati.
Along with their fifth overall selection, the Dolphins own two other first-round picks. The Dolphins acquired the Pittsburgh Steelers' 2020 first-round pick (No. 18) by trading safety Minkah Fitzpatrick and also obtained the Houston Texans' first-rounder (No. 26) in a preseason trade that sent away left tackle Laremy Tunsil and wide receiver Kenny Stills.
The Dolphins' quarterback situation is as fluid as any other position on their roster. Veteran 37-year-old Ryan Fitzpatrick started the majority of 2019 because 2018 10th overall pick Josh Rosen largely underwhelmed.
Burrow is the most hyped prospect in the 2020 draft class after recording one of the best college football seasons ever by a quarterback. The Ohio native led LSU to an undefeated season and national championship.
Burrow set an SEC single-season record with 5,671 passing yards and an FBS all-time record for touchdowns in a single season with 60.