"As I sit here talking to you guys I still don't have my results from Friday's test," Doolittle said on a Zoom call with reporters on Sunday.
"I got tested again this morning without knowing the results of my test from Friday.
"So we've got to clean that up, right? So that's one thing that makes me a little nervous."
Doolittle's comments came on the same day that Nationals manger Dave Martinez announced that two players from the World Series champions had tested positive in intake testing on Friday.
Martinez said the unnamed players had not been to Nationals Park, where the team has begun pre-season training in preparation for Major League Baseball's projected season start on July 23.
"It definitely hurts," Martinez said. "One, you think about the player. Two, right away you think about families -- if they have kids -- and hope that they're all OK.
"For me, I just hope that they come out of it OK and they're back with us as soon as possible."
While Doolittle said he was leaning toward playing this season, he said his health would be his priority.
"If I start to feel unsafe, if it starts to take a toll on my mental health, with all the things we have to think about and this cloud of uncertainty hanging over everything, then I'll opt out," he said.
MLB and the players' union announced on Friday that 31 players and seven club staff members had tested positive among more than 3,100 samples taken in the first round of mass testing undertaken to prepare for the start of the delayed season.
But more positives are popping up as clubs announce their own results.
The Chicago White Sox said Sunday that two players tested positive. The White Sox did not name them, but said they were asymptomatic and had been isolated in Chicago.
"The health of our players and staff is our top priority, and the White Sox are adhering to all MLB health and safety protocols," the White sox said in a statement.
Sunday's announced positives come a day after the Atlanta Braves said that four players -- first baseman Freddie Freeman, pitchers Will Smith and Touki Toussaint and utility man Pete Kozma -- had tested positive.
- 'Ton of bricks' -
Freeman tested negative on the intake test earlier in the week. He developed symptoms afterwards and tested positive on Friday.
Freeman's wife, Chelsea, posted on social media that her husband had several of the major symptoms including "chills and a high fever."
"He is someone who literally never gets sick and this virus hit him like a ton of bricks," she wrote.
As the Braves announced those positive tests, veteran pitcher Felix Hernandez -- who signed a $1 million non-guaranteed contract with Atlanta in the offseason -- announced through his agent that he would opt out of the abbreviated season.
Hernandez became the second Cy Young winner to opt out of the season Saturday, along with Dodgers left-hander David Price.
MLB is aiming to play a shortened 60-game regular season followed by playoffs with all contests in teams' regular ballparks.