Quoting sources, the newspaper reported that Presinal even stayed in the same room as Yuri Sucart -- the cousin identified as the one Rodriguez said acquired and injected him with steroids in 2001-03 while he was with the Rangers.
Late Friday, The Associated Press reported that Major League Baseball investigators want to talk with Rodriguez about Sucart and Presinal.
The interviews were disclosed by a person familiar with their plans who spoke on condition of anonymity because MLB wasn't confirming the meetings. MLB wants to find out if Rodriguez still associates with Succart.
Speaking to reporters after the Yankees' workout at George M. Steinbrenner Field, Rodriguez said that he was not prepared to comment.
"Not for now," Rodriguez said. "Right now, I'm really focusing on taking it one day at a time and getting ready to play. I'm not reacting."
In an interview with ESPNDeportes.com in the Dominican Republic, Presinal said: "I did work with Alex during that period of time [2001 through 2003], just like I helped all of my fellow Dominicans. He used to look for me. But I wasn't working with him on an exclusive basis. I was rotating between players and teams.
"I have never advised a player [to take steroids]; I have never talked about steroids with any athlete, with any baseball player," Presinal said. "I just wish there was someone out there with the courage to accuse me directly. That will never happen because folks respect me."
Presinal served as a trainer for the Dominican Republic during the 2006 World Baseball Classic. But the Daily News reported early Saturday that he will be banned from locker rooms and other restricted areas when the 2009 edition of the Classic opens on March 5.
Yankees second baseman Robinson Cano is among the numerous Major League stars who have worked with Presinal.
Cano said that he last worked with Presinal after the 2007 season to help rehabilitate an injury, and that "all we did was exercise."
Cano said that he stopped working with Presinal because of a two-hour commute for sessions, but he said that Presinal is well-known in the Dominican Republic and is "great about conditioning guys." Cano was not concerned about being linked to a person of questionable background.
"To be honest with you, I don't care what happened to him in the past," Cano said. "I knew what I wanted, and I knew what I wanted to do. I went down to get better about my injury. I don't really care if he had a problem in the past. I don't care what people say. If I had to go back and work with him and I was hurt, I'd go back. He's a guy that knows what he's doing."
MLB has warned players to stay away from Presinal, the Daily News reported, but sources told the paper that he and Rodriguez had been seen together in New York and Miami as recently as this past fall. One baseball official told the paper that Presinal is "an unsavory character."
"He's never had any association with the Yankees," Yankees general manager Brian Cashman said of Presinal in the story. "Whether he knows our players or has worked with any of our players, I wouldn't be able to confirm that."
The Mitchell Report, released in December 2007, had a section titled, "Canadian Border Service Seizure of Steroids in Toronto, October 2001" that detailed the incident that got Presinal eventually banned from clubhouses.
An unmarked bag that Canadian Border Service officers found to contain steroids, syringes and clenbuterol, a stimulant, was claimed by an associate of Indians outfielder Juan Gonzalez, and that person told authorities the bag belonged to Presinal.
Eventually, "Presinal admitted that he had packed the steroids, but he claimed that he carried them for Gonzalez, whom he helped to administer them," the Mitchell Report read. Presinal later denied that to Mitchell Report investigators.
According to the Mitchell Report, Presinal was banned from MLB clubhouses after being seen frequently in the Rangers' clubhouse in 2002. That was Gonzalez's first year back in Texas and Rodriguez's second year with the Rangers. He was later seen in Anaheim and removed, the Mitchell Report said.
Following allegations in an SI.com article that preceded the magazine's release of a cover story, Rodriguez last week admitted to having taken performance-enhancing drugs in 2001-03 while with the Rangers. The fallout has been "kind of what I expected," he said.
Rodriguez said during his news conference on Tuesday at the Yankees' Spring Training facility that his cousin -- later identified as Sucart -- injected him numerous times from 2001-03 with "boli," which he said was intended to give him an energy boost and what he believed to be otherwise harmless. SI reported that Rodriguez failed a drug test for Primobolan and testosterone in 2003.
On Friday, Rodriguez said that he was currently employing no outside help for training, working exclusively with team strength and conditioning coach Dana Cavalea. Yankees manager Joe Girardi said that players working with outside trainers is a continuing concern.
"You don't ever want a player to get hurt when he's working with someone that isn't our people," Girardi said. "Obviously, we feel like we have a pretty good grasp of what they need to do. The players are all going to be a little different and have their own things they like to do, but when you start going to outside sources, sometimes it's hard to manage what they're doing."
Rodriguez said that he has to now consider the company he keeps, needing to pay close attention to such matters "for the next 18 months to 24 months" as his saga continues.
"This is uncharted territory for me," Rodriguez said. "So far, I feel good, just because I'm back on the field and getting ready for the season. We have a very good team, and we have one goal this year."