Tier 2: The runners-up
10) Toronto Blue Jays
9) Boston Red Sox
8) New York Yankees
7) Los Angeles Angels
6) Seattle Mariners
We're now entering the teams that I believe have a serious shot, but won't be able to close the door on an Ohtani deal.
The Blue Jays are a team that was recently linked to Ohtani. It was reported by Shi Davidi of Sportsnet that Ohtani "had taken notice of the Blue Jays’ player-development resources and that the idea of adding a third country, Canada, to his prime fanbase carried some appeal for him." The Jays could be desperate enough to spend the money on Ohtani with their recent playoff failures, but they have to pay guys like Vladimir Guerrero Jr. and Bo Bichette soon, so it's hard to see them also giving Ohtani his megadeal.
The Red Sox are another team that's been linked to Ohtani recently, as Ohtani has a deal with New Balance out of Boston. The Sox can certainly afford to pay him and have the history of winning, but have a roster that has finished in last place in three of the last four years and have an inexperienced President of Baseball Operations running things now in Craig Breslow. It's not impossible, but not likely.
The Yankees are going to be linked with every big free agent. They're a team that's always coveted Ohtani, and I'm sure Shohei is at least intrigued with the idea of going to New York. The problem with them is that they already have a ton of future money tied up in players like Giancarlo Stanton, Aaron Judge, Carlos Rodon, and Gerrit Cole. With New York not being the spenders they once were, it's hard to see them adding a player of Ohtani's salary to that list.
The Angels are a team Ohtani is clearly comfortable with. They let him do his own thing, they already nursed him through one Tommy John Surgery, and he's become a legend with the team. They haven't won anything which makes him leaving likely, but Arte Moreno is going to want him back badly for the money, and Ohtani definitely likes it in Southern California. Again, not likely, but not impossible.
The Mariners have the pitching to carry them but lack the middle of the order bat to pair with Julio Rodriguez. Ohtani, of course, can be that guy. Whether Seattle will pay enough to compete with the top teams remains to be seen, but they were a team Ohtani considered the first time around and have only improved their stock since.