So according to: http://www.spotrac.com/cap-tracker/nba/2015/

This is the cap for teams next year before they sign any of their FAs. The cap is supposedly to increase by 5M (to 68M) next year. This means that the teams below the Pelicans probably* could sign him out right if they wanted to.
Anyone above the Pelicans, like for the Suns, their 62.5M, if they traded PJ tucker for Monroe then they would drop down to 57M (so they could only offer Monroe 11M start, they would have to include another guy like Toliver from their side and an expiring like Anthony from ours so that they could clear another 3M to make Monroe's start 14M to have a chance to keep him. So, I'm not really looking around at teams who are going to be required to make multiple moves to accommodate long-term...
I also don't really want to look at the teams that have no chance at keeping him, because that doesn't make sense unless they legitimately think they can win the title this year. The Nuggets, Nets, Heat?, Wolves, Wizards, Hornets, Pacers - would not be improved enough by adding Monroe to win a title and could not keep him.
The Cavs, Warriors, Clippers, Bulls, Thunder, Rockets... could all take him for a 1 year rental. Is it likely?
Clippers/Rockets/Cavs can't because their firsts are involved elsewhere (if that's the true asking price). The Bulls are stacked in the frontcourt. Can't see the Warriors doing it since they are going to get Lee back and are beasting. The Thunder could feel the pressure to make this trade, it makes a lot of sense. I will include them.
That means, these are the teams, which make sense? Do they have a draft pick/(my thoughts on their)interest level:
Thunder-yes/maybe
Bucks - yes/maybe
Raptors - yes/no
Magic- yes/no
Lakers - only if Top5 (or to Suns)+Rockets first (if 15-30)/yes
Celtics- yes+Clips/yes
Mavs-yes/maybe?
Pistons-lol/lol
Grizzlies-only if 1-5 or 15+ (or to Cavs)/no*
Knicks-lol/yes
Hawks-yes+rights to swap with Nets/yes
Spurs-yes/yes
Blazers-yes/yes
76ers-yes+Heat first (if 11-30)/no.
Now who are these teams Free Agents/would they trade for Monroe:
Red=No
Orange = Maybe
Blue=Yes
Thunder: Perkins, Collison*, RFA Jackson, Thomas, Smith. - This would be a 1yr rental
Bucks: RFA Knight, Middleton, Marshall .. so, we'd have to take someone back to help them in keeping Monroe probably. Problem is Monroe doesn't really fit defensively, plus Parkers injury last night, they could be ready just to fall back into the lottery and get a good player that way instead of trying to move forward this year.
Lakers: Nash, Lin, Boozer, Henry, Price, Johnson*, Ellington - Okay, if they actually had the Rockets pick now this could make a lot of sense, but they don't. So they would just sign Monroe outright.
Celtics: Rondo*, Thorton, Bass - 46M+3M for their first let's say+14M Monroe, they'd probably have to move Rondo, or we could help. They might need to make a 2nd move. Good fit.
Mavs: Chandler*, Wright*, Greg Smith, CVill, Jefferson, Crowder*, Barea - If they could get Crowder/Wright/Chandler on reasonable deals, this could work out. /they might be able to sign him outright.
Knicks: yeah, they would just sign him.
Hawks: Millsap, Carroll, Brand, Antic... so if they think they are going to lose Millsap/want to get younger or a better fit, Monroe's contract would fit easily with Millsaps money and cap room. Good Fit.
Spurs: Duncan, Ginobili, RFA Green, RFA Leonard, Belinelli, Baynes, Ayers, Daye, Joseph, Bonner. Depends on what Duncan/Ginobili do after the season and how willing the organization is to pay for Green. This still works since they're a contender and this move could help them lock up another title. Good fit.
Blazers: LMA?, Matthews*, Lopez, Robinson, Wright, Freeland, Claver, Barton - what the ****. my head hurts. I'll say no.
So, I see 3 teams that would trade for him. 2 that might/I would understand. and 3 that would just sign him this offseason if they wanted him.
So, if you had to vote, where do you think Monroe would be traded to?