Citing sources it said had knowledge of the negotiations but were unauthorized to speak publicly, the newspaper said Selig is expected to hand down a lifetime suspension to the third baseman Thursday or Friday, and about eight other players are expected to be suspended for 50 games.
The expected suspensions come after an investigation into Biogenesis, a Miami clinic accused of providing performance-enhancing drugs to as many as 20 Major League Baseball players.
"I hope he does it,'' former Commissioner Fay Vincent told USA Today. "It's right for baseball. The harder he comes down, the better it is for baseball.''
David Cornwell, Rodriguez's attorney, said the player will appeal any suspension handed down by officials.
MLB said July 22 Milwaukee Brewers outfielder Ryan Braun has been suspended for the remainder of the season for violating anti-doping rules.
The five-time all-star succeeded in having a 50-game suspension overturned last year, but admitted last week he violated baseball's labor agreement and its Joint Drug Prevention and Treatment Program.
Notable deaths of 2014 [PHOTOS]
LeBron James reveals his new Nike shoes