Their thinking is that Manny was unhappy the Red Sox hadn't offered him a new contract, so he took himself out of the lineup with injuries team doctors couldn't detect. He got his wish, both in getting traded to the Dodgers and in being signed to a $45 million extension.
To take a chance on Ramirez at age 41 is to go into the deal with eyes open. Manny has been one of the great offensive players of the past 50 years, and if he has anything left in the tank, he can help a Yanks team desperate for offense.
On the other hand, Manny is different. Sometimes, he's funny and playful. Sometimes, though, he can be infuriating.
However, there's also an easy case to be made for the Yankees giving Manny a shot. Or the Kansas City Royals, who also need offense. They've got one of the best pitching staffs in the game, but it's probably not going to be enough to get them to the playoffs. Ramirez would make the Royals more interesting, and he might make them better, too.
Manny might be the best option for either team, since either could pencil him in as their designated hitter and give him a chance to prove himself all over again.
The Nationals, Dodgers, Pirates and Phillies could also use some offense, but it's tough to imagine Ramirez playing the outfield at his age. Stranger things have happened, but it seems way more comfortable to view Manny strictly as a DH.
Neither the Yanks nor the Royals is likely to be able to land an impact bat at the Trade Deadline. For one thing, at least 20 teams are likely to be still be in contention on July 31, and the last thing any of them will do is start dismantling their club.
If there's an offensive player on the market, the bidding is going to be fierce. At the moment, the Yankees simply may not have the Minor League talent to swing such a deal.
And the Royals, who do have kids, have already traded their best hitting and pitching prospects, Wil Myers and Jake Odorizzi, to get James Shields and Wade Davis from the Rays.
Royals GM Dayton Moore would have to be convinced a trade would land his club in the playoffs before surrendering more of his Minor League talent. Ramirez comes at no cost. He likely will get a low base salary and plenty of incentives. He almost certainly would not land a deal beyond this season. So why not?
The A's saw Ramirez as a low-risk, potentially high-reward signing before the 2012 season. He had to know he would never get huge money again, so he was playing only because he clearly still loves the game. Manny was on his best behavior in Spring Training and then hit .302 in 17 games at Triple-A.
By the time Ramirez had served a suspension for a positive performance-enhancing drug test -- his second -- and played those 17 games, the A's had a logjam of outfielders and granted his request to be released. No other team was interested. (Manny hasn't played in the Major Leagues since appearing in five games for the Rays in 2011.)
Ramirez has been terrific in Taiwan this season, hitting .352 with eight home runs before leaving his team. How those numbers would translate in the Major Leagues is what teams are attempting to figure out.
Manny almost certainly would prefer to play for his hometown team, the Yankees. And what do the Yanks have to lose? Like the A's, they can build protection into the contract and release him if something goes wrong.
Here's where Cashman can lean on the franchise he has built. In going for Vernon Wells, Lyle Overbay, Travis Hafner and others, Cashman went for guys with a team-first attitude who would understand that playing for the Yankees is a privilege.
Manny is a lot of things, but dumb isn't one of them. He knows what the Yanks represent. Ramirez surely would know that they could provide him with the opportunity to put a better finishing touch on his career. He would also know they wouldn't put up with him misbehaving.
Only the Royals, Mariners and White Sox have scored fewer runs than the Yankees in the American League. Derek Jeter, Alex Rodriguez, Curtis Granderson and Mark Teixeira could return in the second half of the season, but there's no way of knowing how much they'll contribute.
Despite everything that has gone wrong, the Yanks are still positioned to win the AL East, and that's what makes Manny a fascinating possibility.
Ramirez would create a flurry of excitement, and that's not necessarily a bad thing. Whether that's all he'd add is the question Cashman surely is trying to answer. He has nothing to lose by finding out.