Both Clemens and Bonds will be eligible for the first time starting in 2013.
"You're talking about, in my opinion, probably the best pitcher of all-time and the greatest player of all time," Palmeiro said. "Keep them out and then the Hall of Fame has no credibility."
Palmeiro, who was suspended 10 games by Major League Baseball in 2005 after testing positive for stanozolol, an anabolic steroid, said he's proud of his career and how he played, even if he's denied a spot in the Hall of Fame.
Palmeiro was voted on just 11 percent of the ballots in his first attempt into the Hall of Fame in 2011. He received 12.6 percent in 2012, well short of the 75 percent needed from voting members of the Baseball Writers Association of America. And he seems to understand it's unlikely he'll get enough votes to make it to Cooperstown.
"I put that behind me already," said Palmeiro, who was in Arlington after being voted by the fans as one of the greatest Rangers of all time as part of the club's 40th anniversary celebration. "I know what kind of career I had. I'm good with it. I can look at myself in the mirror and feel good and proud of what I accomplished. The Hall of Fame would be icing on the cake, but if it doesn't happen, I'm fine with it. I will accept that and move on and live with it."
Palmeiro didn't discuss specifics about his test on Friday, but he has maintained in previous interviews that a B-12 shot he received while in Baltimore was tainted, causing the positive test.
Palmeiro said his career numbers -- 569 home runs and 3,020 hits in a 20-year career spent mainly with the Orioles and Rangers -- don't even stack up to Clemens and Bonds, two others who played during the game's steroid era.
"We're talking a different level of player," Palmeiro said. "Clemens and Bonds, 10 years before they retired they were the best players in the game. These guys dominated the game before anything was ever mentioned about anything.
"So it's going to be interesting. I don't know if they're going to get in or not. But I'm sure they'd say the same thing. They didn't play the game for the Hall of Fame. They played the game because they loved to play the game as kids growing up and it was their career, it was the way they made a living for their families and that's what's important."
Palmeiro, who attended Pudge Rodriguez's retirement news conference earlier this season and said he still goes to many Rangers games, said the game is focused on its current crop of stars and not those from his era.
"Baseball did what they had to do to fix the game or clean the game," Palmeiro said. "So they're moving on. Baseball is bigger than any player that ever played the game. Our era is over with and they're focusing now on the era that's here now and they're improving the game, which is the important thing."