Washington acquired Papelbon from Philadelphia on July 28 and installed him as the closer ahead of Storen, who at the time owned a 1.73 ERA and had converted 29 of 31 save opportunities. Storen pitched well for his next five appearances, but he allowed 14 earned runs over 13 2/3 innings the rest of the season.
After Storen's final outing, on Sept. 9, he slammed his locker shut in frustration and suffered a non-displaced fracture in his right thumb, ending his season. The 28-year-old is now heading into his final year of club control and will be due a raise from $5.7 million through arbitration.
"I also think Storen is going to pitch much closer to the guy before the last month of the season than he will the guy in the last month," Rizzo said. "It's important for him to pitch well personally and important for us. He's got good stuff, and there's no reason he should not pitch well."
In 22 games with the Nats, Papelbon posted a 3.04 ERA and converted seven of nine save opportunities. His season ended on Sept. 27, when he initiated a physical altercation with teammate Bryce Harper in the dugout, resulting in a team suspension. Papelbon is set to make $11 million in 2016, the final year of his contract.
"I don't see any lingering problems with Papelbon and Harper," Rizzo said. "They're both competitive guys and they both want to win. Having both of those guys on the team will help us win. They've spoken, and I think we've made a bigger deal out of it than they ever did. I think they're going to be fine."
Even if Papelbon and Storen both stay, the bullpen should be an area to address after faltering down the stretch as the Nationals fell short of the postseason. Casey Janssen and Matt Thornton are both free agents, Craig Stammen and David Carpenter are coming off injuries, and Aaron Barrett likely won't return until at least September after having Tommy John surgery.
Rizzo said the Nats will be open to adding pieces either through free agency or trades.
"With the depth we have, we think the trade market might be a good market for us," he said. "But with that, you always have to balance what you're giving up for the future with what you're getting for the present."
Andrew Simon is a reporter for MLB.com. Follow him on Twitter @AndrewSimonMLB. This story was not subject to the approval of Major League Baseball or its clubs.