Sources told ESPN's Outside the Lines that 12 other players also will be suspended on Monday.
MLB has had no comment on the various reports.
"I think we all agree that we want to get rid of PEDs," Rodriguez said. "That's a must. I think all the players feel that way. But when all the stuff is going on in the background, and people are finding creative ways to cancel your contract and stuff like that, that's concerning for me, that's concerning for present, and that's concerning for future players as well."
Rodriguez told reporters, "There's more than one party that benefits from me not stepping back on the field -- That's not my teammates and that's not the Yankee fans."
When asked to clarify who benefits, Rodriguez responded by saying, "I can't tell you that right now, and I hope I never have to."
The Associated Press and New York Post reported on Friday that discipline will be handed down for nine or 10 players.
It's expected that a majority of the players involved will accept 50-game suspensions that would cost them the remainder of the regular season. According to a report in the Post on Friday, a deadline of 6 p.m. ET on Sunday was set for players who had not yet accepted a deal.
Rodriguez is a separate case, as baseball is believed to be threatening a lifetime ban. If Rodriguez is allowed to return in 2015, he would be able to collect on the last three years of his contract -- worth about $60 million -- in '15, '16 and '17. Rodriguez has retained a Manhattan law firm that has been discussing a possible plea bargain with MLB.
If necessary, two lists of names could be revealed. One would be for players who, like the Brewers' Ryan Braun, tacitly admitted guilt by accepting suspensions. If needed, the other list would be for those who plan to appeal their sentences to an arbitrator. Baseball officials were clearly hoping that they could strike deals with all involved to begin putting the investigation behind them.
Rodriguez, sidelined the entirety of this season due to left hip surgery, hit a two-run homer, drew a walk and struck out for Trenton on Friday. He was scheduled to continue his rehab stint in Trenton on Saturday at 7:05 p.m. against Reading. If Rodriguez is not suspended and prevented from playing pending an appeal, the "tentative plan" held by general manager Brian Cashman and the Yankees is to activate the third baseman from the disabled list for Monday night's game against the White Sox in Chicago.
Multiple reports have indicated that the evidence will include that A-Rod not only acquired performance-enhancing substances from Biogenesis but that he recruited other players to patronize the clinic and impeded MLB's investigation.
Other names that have been linked to the investigation include Tigers shortstop Jhonny Peralta, Rangers outfielder Nelson Cruz, Yankees catcher Francisco Cervelli and Padres shortstop Everth Cabrera.
Braun, the star left fielder, accepted a 65-game suspension on July 22. If there are any appeals, MLB would present that as evidence to support the credibility of Biogenesis founder Anthony Bosch, who agreed to cooperate with baseball's investigators.
A player who accepts an immediate suspension technically would be eligible for the postseason if his team makes it. As a practical matter, though, it would be nearly impossible for a player to be sharp enough to contribute at that point.
When Giants outfielder Melky Cabrera was suspended last year, he could have been activated in time for the National League Championship Series, but the Giants decided against the move. Manager Bruce Bochy explained at the time that he liked the way his roster had pulled together down the stretch.
Though he did test positive in 2003 survey testing, Rodriguez never has tested positive for PEDs in non-survey testing, which could help his case in any appeal. But if it comes to that, arbitrator Frederic Horowitz will have the latitude to consider a lifetime suspension and perhaps impose a lesser penalty.
Cashman declined to speculate on the future during a conference call with reporters on Wednesday. He referred all questions to MLB, adding that the team will continue to assume Rodriguez will return to active duty until told differently.
"I think you have to at this point," Cashman said. "Nothing's been handed down, so I think you have to. We expected to have him back at this point. We don't have him yet, but I know he's playing in a simulated game [Thursday], and that's a step in the right direction."