The Marlins transferred Nardi (elbow) to the 60-day injured list Saturday.
The Marlins placed Nardi on the 15-day injured list, retroactive to Thursday, due to a left elbow injury.
Nardi collected his 12th hold of the season in Wednesday's win over the Rays, walking one and striking out three in a scoreless sixth inning.
Nardi might step into the closer role if Tanner Scott is traded, Kaushik Sampath of the Miami Herald reports.
Nardi picked up his seventh hold of the season Sunday, giving up a hit and striking out a batter to record the final out of the seventh inning.
Nardi gave up a hit and a walk in a scoreless inning Friday while striking out one, but he was charged with his third blown save of the season after allowing an inherited runner to score.
Nardi struck out the side in a perfect eighth inning Sunday to record his third hold of the season in a loss to Atlanta.
Nardi struck out two in a perfect seventh inning during Sunday's win over the Cardinals.
Nardi walked one in a scoreless inning of relief during Friday's Grapefruit League game against the Cardinals.
Nardi recorded his third save of the season in the second game of Wednesday's doubleheader against the Mets, walking one and striking out two in a scoreless ninth inning.