Their highest paid player is about to move up another rung to approach the top of baseball’s most revered record, yet the New York Yankees organization appears embarrassed by the situation and legally and financially conflicted.

It’s hard to blame them.

Alex Rodriguez entered Friday night’s game just three dingers short of passing Willie May’s 660 home runs. The Yankees are home for six straight games. The achievement will move him to fourth on the all-time career HR list. Holding the record of 762 is Barry Bonds, who, like Mr. Rodriguez, was beefed up on steroids for a good number of those trips around the bases.

Second is Hank Aaron, with 755, considered by many to be the legitimate home-run king. He is followed by the highest deity in the Yankee pantheon, Babe Ruth, who appears to have restricted his substance assistance to beer and hot dogs.

Under normal circumstances, one would expect the Yankees to be geared up to monetize and memorialize the 661 home runs with T-shirts, posters and other paraphernalia, plus on-field salutes from past Yankee greats and perhaps the Say Hey Kid himself, the 83-year-old Mr. Mays.

As things now stand, it looks like none of that will happen. The Yankee media machine is largely ignoring the approaching achievement. And it does not seem excited that Mr. Rodriguez is 48 hits from 3,000, either. Recall that the enthusiasm (and marketing) was already building when Derek Jeter was 100 hits from that milestone.

The overwhelming consensus, however, is that Derek Jeter never used steroids. Mr. Rodriguez was caught multiple times and lied about it. There is the difference. Mr. Rodriguez returned this season after a yearlong steroid-use suspension.

In addition to ambivalence about recognizing the achievements of a tainted star, the Yankees face legal considerations. The 10-year, $275 million contract Mr. Rodriguez signed in 2007 includes a $6 million bonus each time he reaches one of the top-four home run totals, with another $6 million for passing Mr. Bonds, which seems unlikely.

The Yankees had planned to exploit the marketing opportunities. Now their product is contaminated and there is speculation the club will try to void the bonuses, citing the cheating. They will probably have to pay up.

Mr. Rodriguez’s return at age 39 has been remarkable. His .419 on base percentage is 10th in the league, his four home runs eighth and his 11 RBIs, 14th.

How bizarrely awkward this is for the Yankees, and deliciously entertaining for everyone else.