Everyone is ignoring the fact that A-Rod has a full no-trade clause and at least in his postgame interview after Game 4 he told the reporters that he won't be leaving NY. I'm not saying he absolutely wouldn't accept a trade anywhere, but if I'm him I'm probably loathe to accept a move to the Cubs. Would it be best for him to leave the Yankees? Almost definitely. But his pride might not allow it until he feels he has proven himself one more time in NY.
FWIW, he hasn't been better than a $6-$8M 3rd baseman, even when on the field, since 2009, arguably even 2008. Jeter had about a year and a half down until he learned to adjust. A-Rod has had at least 3 years of increasing struggles with a slowing swing and has shown no inclination whatsoever to adjust his approach. He needs to get shorter to the ball, try to hit it the opposite way with 2 strikes. He can't catch up to a good fastball anymore, at least not to pull it in the air. Until he accepts that fact he's never going to bounce back meaningfully. I think this is another pride issue - he still thinks he should be A-Rod and should be able to turn on the inside fastball and punish pitchers for throwing it the way he used to when he was 28 and a stud. He can't do it. Until someone convinces him of that we'll see a lot of days like what he had in the playoffs, particularly against pitchers who throw as hard as the Tigers guys do.