Girardi, 29, is in the final year of his current contract and can become an unrestricted free agent next summer.
The NHL is currently in a roster freeze, which is lifted at 12:01 am, Dec. 28.
Several teams have expressed an interest in Del Zotto, but the Rangers are looking for upgrades and want to package Del Zotto in a deal for a top-tier player.
According to the Sun, the Rangers are willing to entertain calls for just about anyone except Rick Nash, Henrik Lundqvist and Chris Kreider.
The Rangers had been fielding calls for Kreider earlier in the season, but it appears he's no longer on the block.
Sather would like to keep Girardi, but he might be entertaining offers if he finds himself unable to sign the former All-Star to a contract extension.
In 36 games with the Rangers so far this season, Girardi has collected two goals and six assists for eight points, and has a minus-7 rating.