The Angels are going to stay in play as long as possible for better or worse
Speaking of a team that doesn't have the look of a contender but who also may be desperate to have Ohtani, returning to the Angels is going to remain an option this offseason. LA really wants to keep him around to pair with Mike Trout and they really did try to go for it at this year's trade deadline. While that really didn't work out well for them, it could have showed Ohtani they are committed to competing if he sticks with them.
Unfortunately, the Angels are not a very good baseball team. They cannot develop pitching or even sign competent pitchers, and the offense, even with Ohtani in the lineup, was extremely hit or miss, especially with Trout dealing with injuries yet again. LA will certainly try to build a roster to try and bring Ohtani back, but they aren't among the favorites to land him right now.
The Rangers are all-in and they covet Ohtani
Fresh off a World Series win, Texas' strategy of going big in free agency and the trade market the last couple of years has been vindicated. They have already brought in Corey Seager, Marcus Semien, Jacob deGrom, Nathan Eovaldi, Jordan Montgomery and Max Scherzer in the last calendar year. While the deGrom signing was a bit of a whiff as he got hurt (as did Scherzer), a lot of those guys were a big reason why the Rangers were able to take the title home.
Texas has already been mentioned as a potential landing spot for Ohtani likely due to their free-spending ways (and the fact they are certainly going to be good again next season), but there are some problems here. On the marketing side, Texas isn't the greatest place to attract eyeballs. The Rangers are already really close to the luxury tax threshold with a lot of that payroll tied up for a while. They will certainly be players for Ohtani, but there has to be a limit to how much they can spend at some point.