Baseball used to use 1 ball for an entire game and it was never allowed to be kept by fans. that rule change about 100 years ago. It was deemed that it was better for the game and got more people to the games if fans simple kept the balls and it was better for the players to be playing with a new, standardized ball. The league OK'd fans keeping balls a long time ago.
The players understand this as well. Many players offer big rewards in exchange for the ball they want and some players are not so nice about it. A-Rod should be offering a signed balls, bats, jersey and a couple tickets to a game. If he really wants it. You can't offer a person who wants the ball and doesn't care about the ball money. it would have to be offering him a collectable that he would want more.
That being said, I think that if the player offers a reasonable exchange you should do it. do we know what ARod has offered???