With five potential mystery teams, let’s subjectively (power) rank them according to how likely it is that they’re one of the mystery teams of note. This way lies adventure: 
You can very well be a mystery Cole team if you’re a known Cole team. According to layers upon layers of recent reportage, the Yankees, Angels, and Dodgers are the biggest Cole chasers at the moment. Knocking those out gets us down to 27 teams. 
The best part about mysteries is solving them, so let’s undertake an educated effort to that end (while of course allowing for imprecision and generalities). With our phasers set to “process of elimination” let us boldly proceed into the Land of Mystery Teams.
Right-hander Gerrit Cole is the most coveted of free agents right now for a number of reasons, all very good. He’s still on the right side of age 30, he’s proved regularly capable of topping 200 innings, and he’s fresh off a dominant two-season run with the Astros

Let’s get rid of the known Cole suitors

That would be the champion Nationals. They recently re-upped with Strasburg at great cost, and they have a front four of Max Scherzer, Strasburg, Patrick Corbin, and Anibal Sanchez. To repeat from this and every rooftop, every team could use Cole, and that includes the Nats. However, their rotation is perhaps the best in baseball, and their remaining budget will be spent re-signing third baseman Anthony Rendon or — far more likely — a replacement for Rendon. As well, the Nats are operating with one eye on that CBT threshold. Eight teams. 

Let’s get rid of the non-spenders and rebuilders

Some teams qualify as fringe contenders or at least “squint and you can see them mattering,” but they’re either insufficiently committed or insufficiently equipped to pay the going rates for Cole. Under this phylum, we’ll stow away the Rockies, Reds, Diamondbacks, Mets, and Braves. In the Braves’ case, addressing the third base situation seems to be the priority, and like a lot of teams they seem unlikely to stomach a 0 million investment in one player. Now we’re down to 12 teams. 

Let’s get rid of those who are only sort of trying

The Competitive Balance Tax (CBT, or luxury tax) threshold serves as de-facto soft salary cap in MLB, and a couple of teams are close or over that 8 million line and either angling to get under it or stay under it. The Cubs, Red Sox, and incumbent Astros go here. Now we’re down to nine teams. 

Let’s get rid of those who don’t want to spend more

First, the Twins. Minnesota is reportedly interesting in plucking from the next tier of free-agent starters — i.e., Madison Bumgarner, Hyun-Jin Ryu, and Dallas Keuchel — but it’s hard to imagine that they’ll shop in Cole’s range. Let’s also include the Cardinals. They’ve been linked to Bumgarner, and it would indeed make sense, as they could use a 200-inning stabilizer at the front end. They’ve also got a bit more than million to spend while still stay under the CBT borderline. That’s enough to pay Bumgarner (or Ryu or Keuchel), but Cole won’t fit within that figure. Six teams. 

Let’s get rid of the team that won’t add more starters

Mystery solved? Lol, no. Mystery pontificated upon at length? Achievement unlocked. Anyhow consider one or two of the five teams just above to be the mystery team or teams who endeavor to elude us like the spectral presence of Carmen Sandiego wearing Waldo’s stupid blend-in nerd clothes.

Let’s get rid of teams who won’t pay this much for rotation help

Even though we’ve enjoyed a comparatively frenzied pace this offseason — and even though Stephen Strasburg is already off the board — the market for Cole is still taking shape, even if that shape has some form to it. Just when we thought the serious bidding was down to three squads, Jon Heyman on Tuesday reported that a “mystery team” is in on Cole. Soon thereafter, Cole’s agent Scott Boras declared the existence of not one but two mystery teams. Two! Sure, the mystery team phenomenon is fertile ground for mockery, but out-of-nowhere signings of major free agents do happen. It’s entirely possible there’s something to it. 

Let’s eliminate the Blue Jays

Cole’s going to command an eight- or nine-year deal, probably in excess of 0 million. While teams are rolling in revenues these days and franchise valuations are soaring, not every club is willing to invest in the on-field product to such an extent. Additionally, some teams are in various stages of rebuilding, which means Cole won’t be on their radar (even though Cole qualifies as a near-, mid- and long-term play). This safely allows us to eliminate the Athletics, Brewers, Rays, Indians, Marlins, Royals, Tigers, Orioles, Mariners, and Pirates. Now we’ve whittled it down to 17 teams. 

Now let’s rank the last five standing

Sorry, Blue Jays, you’re out. They should absolutely be adding starting pitching to an impressive young core of position players, and there may be a willingness to hand out a nine-figure contract. However, it’s hard to imagine that the Jays, especially under Mark Shapiro, will spend at those levels. Five teams.  As a former No. 1 overall pick, Cole necessarily has dominant stuff and a full repertoire, and on Houston’s watch he ramped up his spin rate. That helped him author a truly dominant 2019, in which he led the majors in strikeouts and ERA+. What bodes especially well for the future is that Cole this past season struck out 39.9 percent of opposing hitters. Among qualifiers, that’s an all-time single season record. All of this is to say: Every team can be made significantly better with the addition of Cole, no matter how strong their current rotation. Every team, however, will not be in on Cole.