Speaking at the General Managers Meetings at the Hyatt Regency Indian Wells, Rizzo conceded that Mike Morse or Jayson Werth could move into LaRoche's spot if needed.
"We have other options so that makes it less critical," Rizzo said. "But because of what he means to the team, how he balances the lineup, the type of defense he gives us and his leadership, it makes him an important guy for us to lock up."
LaRoche, 32, hit a career-high 33 homers, tied his personal best with 100 RBIs and won his first Gold Glove Award this year. Washington led the Major Leagues with 98 wins and won the franchise's first division title.
The Nats made the $13.3 million qualifying offer in order to receive Draft-pick compensation if LaRoche signs elsewhere, but their hope has always been to keep him in a Washington uniform with a multiyear deal.
Rizzo said he wasn't worried that LaRoche testing the market will decrease the team's chances of having him back in 2013.
"I don't think it lessens it. I think it will show him and I what his true value is in the market, and we'll see if there's a fit for us," Rizzo said. "We've been in contact [with his representative]. We've touched base a couple times since the season ended. We continue to talk and we'll see where it leads us."
Rizzo added that those negotiations won't hinder him from addressing other issues.
"You have to be versatile in your thinking," Rizzo said. "You have to have different avenues to go, and when one door slams, another one opens. You have to be open-minded and kind of quick on your feet, and figure out the landscape at any given time."
Paul Hagen is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.