"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."
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."
Maddon on Arrieta: 'His focus is off the chart'
Before Tuesday's Cubs game Joe Maddon talked about the performance enhancing drug suspicion that surrounds a player like Jake Arrieta when his success becomes so great.