Zimmermann and Desmond have until 5 p.m. ET on Nov. 13 to make a decision on their offers, which they are expected to decline. The qualifying offer for each is a $500,000 increase from the $15.3 million that was put into play after the 2014 season.
By making a qualifying offer, a club is guaranteed a compensatory Draft pick -- that pick would come at the end of the first round -- if a player rejects the offer and signs with another club in free agency.
Desmond is coming off a down season, during which he hit .233 with 19 home runs, 62 RBIs and 13 stolen bases. The Nationals tried to sign Desmond to a seven-year extension worth $107 million in early 2014, but Desmond turned it down.
After going 0-for-2 with a walk on the last day of the season against the Mets, Desmond had tears in his eyes and had a tough time putting the words together as he tried to say goodbye.
"When I got drafted by the Expos, they didn't know where the team would be," Desmond said. "But they couldn't have found a better home. ... I'm extremely proud to say that I was a Washington National."
As the tears were flowing, Desmond was asked if he wanted to stay with the Nationals.
"At the particular moment, there are a lot of things to be discussed," he said. "This organization has been nothing but good to me. We have come a long way, not only personally, but as an organization."
Zimmermann, who won 13 games in 2015, also turned down a contract extension prior to the season. Asked last month if he would be back with the Nationals next season, Zimmermann said, "I'm not sure. I can't really answer that. Every team is going to have a shot. We'll see this offseason what happens if they come calling."
Span is coming off an injury-plagued season, but is considered the best leadoff hitter in Nationals history. His best season was in 2014, when he hit .302 and scored 94 runs.
Span said Friday he is open to returning to Washington, but the ball is in the Nationals' court. Span, who is represented by agent Scott Boras, is coming off hip surgery. He is expected to start jogging in a couple of weeks and should be able to ease into baseball activities a few weeks after that.
Fister is not in the Nationals' plans. He started the season in the rotation, but lost his job in August to right-hander Joe Ross. Fister spent the rest of the season as a long man in the bullpen. He said he would like to be in a starting rotation next season.