Lifelong Yankees fan. Of course I care.
As for the next, Pudge is 39 and has 25 hits this year. He's no longer an every day catcher, and will need at least 2 additional seasons to get there, unless someone wants a guy hitting .214 as their every day catcher.
Next is Omar Vizquel, who's 169 hits short as of yesterday and is 44 years old. No longer every day. No.
ARod is a year younger than Jeter, and the bum knee isn't doing much to his hit count (though, if he opts for surgery, which he should, he may miss July). He's not going anywhere, and should hit 3k potentially by the end of the 2012 season, but likely by early 2013.
Damon... could possibly get there. He's 37 and has over 100 hits once since 2006. He's ~340 hits short now, so he'd need over 3 seasons. It's probably more of a question if he can find someone to sign him.
Chipper's 435 hits short and is 39 with health problems. He's a HOFer, but I don't think he gets there.
Looking at the rest of the list (
http://www.baseball-reference.com/leaders/H_active.shtml), I think it'll be Pujols after ARod.