So, which teams would be interested in acquiring Monroe? Thankfully, we can survey ESPN's NFL Nation reporters about who could need a starting left tackle.
Here are some possibilities:
San Diego Chargers: San Diego could be in the market for an upgrade. King Dunlap is 30 and injury-prone. Some thought the Chargers would take an offensive tackle with the No. 3 pick (Ronnie Stanley became a late rumor), but San Diego ended up not taking an offensive tackle in the draft.
Seattle Seahawks: Monroe's $6.5 million salary could make a trade to Seattle unlikely. The Seahawks have a total of $11.7 million committed to their entire offensive line in 2016. But Seattle lost Russell Okung in free agency, and it doesn't have a proven tackle to protect Russell Wilson's blind side. Right now, Seattle seems content in moving Garry Gilliam to left tackle and plugging in J'Marcus Webb at right tackle. A plus is Monroe has experience in a zone blocking system.
New York Giants: The Giants brought in Okung for a free-agent visit in March, so they have shown interest in adding an offensive tackle. Ereck Flowers is the starting left tackle for now, and the Giants wouldn't have used the No. 9 pick on him last year if they didn't see him as a left tackle. But it probably wouldn't kill Flowers' development to play a year or two at right tackle while a more experienced player started on the left and mentored him.
If a team traded for Monroe, it would take on his $6.5 million base salary, which ranks ninth among left tackles. There are 24 teams that have enough cap space to add Monroe, including the Chargers, Seahawks and Giants. Baltimore would carry $2.2 million in dead money in 2016 and $4.4 million in 2017.
Monroe, 29, had been a solid and dependable left tackle for his first five seasons in the NFL. But multiple injuries forced him to miss 15 regular-season games over the past two years. Monroe also has been outspoken about getting medical marijuana off the NFL's banned substances list, which could turn off some teams.
What could the Ravens get for Monroe? In April, the Denver Broncos traded offensive tackle Ryan Clady and a seventh-round pick to the New York Jets for a fifth-round pick. Baltimore could hope for a similar deal.
Information from ESPN's Sheil Kapadia, Eric D. Williams and Dan Graziano was used in this article.