Square jawed trannies, Madonna, steroids and hookers. A-Rod is well on his way to the Hall of Fame.

[www.nydailynews.com]- A former Manhattan madam who supplied Eliot Spitzer with hookers also counted Yankee slugger Alex Rodriguez as a customer – and found him so charming she dated him herself for free, former employees of the call-girl agency tell the Daily News.

A-Rod wooed ex-madam Kristin Davis with flowers, jewelry, persistence and heated e-mails, according to the sources.

“Throughout the years, there were a number of clients that I befriended and it was not uncommon for them to want the women they can’t have whether it be the phone bookers or the madam,” Davis said.

“In regard to Alex, all I can say is our paths have definitely crossed personally and professionally.”

Davis met Rodriguez in June of 2006 in a gym in Philadelphia, shortly after she opened a branch of her call-girl service in the City of Brotherly Love, sources said.

Davis told a friend the then-married Rodriguez asked her, “What are you doing tonight?”

The shapely madam didn’t know who A-Rod was but found him “hot as hell,” she told the friend. “I said, ‘I’m having dinner with my boyfriend. But if you’re looking for someone to hang out with, here’s a number.’ I gave him my agency’s card.”

That night, Davis told a friend, Rodriguez booked a two-hour “date” with one of her girls, who met him at the Four Seasons on Rittenhouse Square.

“He gave his real name,” Davis told the friend. “The next day we found out who Alex Rodriguez was. The girl we sent freaked out. Her father (works for) another Major League Baseball team.”

Rodriguez soon became a repeat customer of one of Davis’ three Manhattan agencies, two former employees said.

In an e-mail exchange provided to The News by a former booker for Davis’ Wicked Models, Rodriguez purportedly told Davis on Nov. 17, 2006: “Thanks for setting me up with Samantha. She was gorgeous. But she is not you. When can I see you you are gorgeous . . .”

The exchange goes on:

Davis: “Hi Alex. You don’t want to see me. I’m no fun. lol. Just because your (sic) so sweet, here are some pics of me and I appreciate the compliments. Your (sic) a doll. Thanks, Kristin”

Rodriguez: “You have been playing hard to get for a year now, your (sic) killing me.”

Davis: “It’s not playing I am hard to get. Maybe you should try harder.”

Rodriguez: “Kristin, I definitely will and I love the pics. I put the one on my cell so I can look at you all the time. Alex.”

Davis: “You are too sweet. I’ll let you know when I get someone you like.”

Two former agency workers said A-Rod hired prostitutes more than a half-dozen times, often meeting them at the Four Seasons hotel on W. 57th St.

“Alex was a very nice client to talk to,” the booker said. “He didn’t like one girl we sent over there. He sent her away. He kept calling the agency.

“He kept trying to reach Kristin. Kristin wouldn’t talk to most of the clients, but she said she’d call him back. She told me, ‘Don’t worry about sending him another girl. I’m going to go over there and have drinks with him, hold his hand. He spends a lot of money.’ ”

The booker said Davis “is not star-struck, but all her boyfriends were Latin. So Alex was her type. And Alex was very persistent. I think he sent her a bracelet.

“Kristin knows how to play men. One time, Alex called the agency in the middle of the night for Kristin. He was at some club or lounge. He said, ‘I’ve been waiting here for an hour. Please tell her to hurry up.’ ”

Rodriguez’ persistence is said to have paid off with the buxom, 32-year-old Davis. Though Davis’ agencies typically charged clients more than $1,000 an hour, Davis told a friend: “Alex didn’t pay me . . . I went out with him just because he was so flattering. I couldn’t not give in.”

On Feb. 9, 2007, Rodriguez purportedly e-mailed Davis: “My sexy blonde girl. When can I see you again? I am addicted to you. Did you get the flowers I sent?”

That e-mail brought this reply: “I received your flowers. You outdid yourself, I feel very adored. Thank you. And I received your other gift today. You really spoiled me.”

A source said A-Rod confided the pressures he felt as a player.

“He told her that he’d used steroids,” the source claimed. “He said a lot of players did. He just wanted to be a good ballplayer.”

Last month, Rodriguez acknowledged using performance-enhancing drugs several years ago.

Davis told a friend she and Rodriguez grew apart “when he found out I had a new boyfriend. He got upset. What was I supposed to do? He was married.”

A spokesman for Rodriguez declined to comment.

Confronted with the e-mails, Davis said, “Other people have had access to my client records as well as my personal information and I can’t control what has been released.”

She declined to discuss “any issues relating to my clients.” Though Davis is selling a memoir on www.manhattanmadam.com, she noted, “With the exception of (former Gov.) Eliot Spitzer, I have not named names….I do not wish to ruin any lives.”

Davis got five years’ probation for promoting prostitution after serving three months in jail.

In 2007, Rodriguez was photographed in Toronto with former stripper Joslyn Morse, who refused to say if they’d had sex. Another stripper, Candice Houlihan, claimed she and the Bronx Bomber had a two-night stand in 2004.

Cynthia Rodriguez filed for divorce last July. Her lawyer said at the time that A-Rod had “an affair of the heart” with songstress Madonna.

An earlier headline on this story incorrectly cited Kristin Davis as a source of claims about Alex Rodriguez. The News regrets the error.