"If you look at it from the macro side, who'd people rather see hit: Big Papi or me?" Scherzer told the website. "Who would people rather see, a real hitter hitting home runs or a pitcher swinging a wet newspaper? Both leagues need to be on the same set of rules."
Scherzer, who said he likes hitting, jammed his right wrist and thumb batting in Thursday's loss to the St. Louis Cardinals. He has only briefly played catch since sustaining the batting injury and missed a scheduled bullpen session Saturday.
"If you look at it long-term, I think eventually there will be a DH in the National League," Scherzer told CBS Sports.
Scherzer told The Washington Post he is "dealing with a little sprain" in his thumb, adding that the swelling increased more than expected Thursday night. The team began treatment the next day.
"I'm progressing every day. I'm literally day-to-day," Scherzer told the newspaper. "I'm making progress every single day from the treatments, doing the hot-cold contrast nonstop, so for me it's just keep doing the treatments and see where this goes."
Washington starts a series at the Atlanta Braves on Monday. Manager Matt Williams said Scherzer will likely be scratched from his scheduled start Tuesday.
"We'll probably have to make an adjustment," Williams said. "I don't anticipate him missing more than one turn."
The defending NL East champions lost their fifth game in a row Sunday. Williams said he didn't know who would replace Scherzer against the Braves.
Scherzer said he wants to be able to throw all of his pitches without pain before he returns.
"Any type of discomfort is going to alter the way I throw the ball," he said. "If I alter the way I throw the ball, I run the risk of major injury to my arm."
Scherzer is 1-2 this season with a 1.26 ERA. He has allowed no more than two earned runs in any of his four starts in 2015.
At the plate, he is 1-for-9, striking out three times.
The Associated Press contributed to this report.