"You would have to have your head in the sand or your head somewhere else not to at least wonder, 'How is he doing this?' " Bayless said Wednesday.
Bayless made his comments while discussing Jeter's season with fellow commentator Stephen A. Smith, who defended the 13-time All-Star.
"I would have to be sight and hearing impaired not to at least wonder, because there is no HGH test in the sport of baseball," Bayless said. "They do not blood test. They do it one time in spring training for HGH, not again the rest of the year. How could I not wonder is he using something? If you're Derek Jeter, would you think about using HGH right now because I would. How would you not? Would you not think about it?"
Jeter responded before the Yankees' 2-1 loss to the Chicago White Sox, saying: "One of the things is that now you have everybody questioning everything. That's the unfortunate thing. Maybe Skip should be tested."
The day of the comments, Jeter homered for the third straight game for the first time in his big league career, but the Yankees were swept by the White Sox in the three-game series.
Jeter had hit safely in 17 of his last 18 games, moving up this week to 11th in career hits and 13th in runs.
"I'm seeing a whole new guy this year," Bayless said. "No way I could see he would be an MVP candidate, that he would be hitting .324 in 2012 as he now goes on age 39. Are you kidding me?"
Before the game, Jeter told reporters he'd never been mentioned in a steroids conversation publicly as Bayless did.
"This is a first for me, man. I don't know what to tell you," Jeter said.