Flames GM Jay Feaster is in the middle of a rebuild, and has already dealt away captain Jarome Iginla and star defenseman Jay Bouwmeester.
Sarich, rearguard Anton Babchuk, left wing Curtis Glencross, veteran Alex Tanguay and winger Lee Stempniak have attracted plenty of interest league-wide.
Some teams, according to the source, have kicked the tires on sniper Mike Cammalleri, but the Flames aren't anywhere near to dealing him.
Several clubs are looking for a defenseman to add to their third pairing, and Sarich has one-year left on his current contract at an annual salary of $2 million.
It's believed a deal could be finalized as early as Tuesday evening.