Stephen A. Smith and Skip Bayless are not accusing Cubs pitcher Jake Arrieta of using PEDs, however they are not turning a blind eye on him based on his sudden rise in performance. (1:56)

CHICAGO -- Cubs pitcher Jake Arrieta, the reigning National League Cy Young winner, said it's "flattering" that some in the game are questioning whether he has used performance-enhancing drugs to achieve his status among the elite pitchers.

"It's somewhat flattering, especially when some of those comments are coming from some of the best players in the game," Arrieta said Tuesday.

Arrieta wouldn't name names but said his teammates have told him other players have wondered whether he is cheating the system. Arrieta is 4-0 with a 0.87 ERA this season, and he tossed his second career no-hitter last Thursday against the Cincinnati Reds. In his last 24 starts, dating back to last regular season, Arrieta is 20-1 with a 0.86 ERA. He came to the Cubs in 2013 from the Baltimore Orioles with a career ERA over 5.00.

"I think it's funny," he said. "I've always been in good shape. I just sucked early in my career from a statistical perspective. My body has always been very similar to how it is now. The results are different, so people want to question things. That's the nature of sports."

With a 20-1 mark and a 0.86 ERA over his past 24 starts dating back to last season, Jake Arrieta said it's "somewhat flattering" that some have questioned whether he's used PEDs. AP Photo/Mark J. Terrill

Arrieta's workout routine is well known for being rigorous, and it includes heavy Pilates. He claims he only eats healthy.

"I challenge anyone to go with him for his workout program for maybe one week -- I won't even say a week, I'll say for two days," manager Joe Maddon said. "Just go keep up with him for two days and see what he actually does and see if you could keep up with that particular workout program."

Not only is Arrieta adamant that he does not take steroids, he said he'd like heavier penalties for those who do.

"That's something I've had a firm stance on for a long time," Arrieta said. "I remember being in Baltimore and talking to the older guys about how we can rid the game of people trying to cheat. A lot of steps have been taken in the right direction."

Arrieta was asked if he would be in favor of a "one strike and you're out of the game" punishment.

"If it's a blatant attempt to cheat the system with a steroid, then maybe so," he said. "It's apparent guys are still trying to take things, and guys will continue to do so unless the penalties are stiffer. I personally don't think guys should get multiple chances when guys fail a steroid test.

"If I'm doing it the right way, I expect everyone to."

Arrieta, whose next start is Wednesday against the Milwaukee Brewers, said he's confident he has done things the right way.

"I think it's flattering," he said. "I know I've never taken any shortcuts and never intend to."