Smith, 26, spent the first four-plus years of his NHL career with the Blackhawks. In 61 games this season, he has nine points (five goals, four assists) in an average ice time of 13:35. In 2013-14, Smith posted career-highs in games (75), goals (14) and points (26).
Smith is due $1.5 million in each of the next two seasons before hitting unrestricted free agency for the 2016-17 season.
Desjardins, 28, spent his last four-plus years with the Sharks, appearing in 56 games this season with eight points (five goals, three assists) in an average ice time of 10:27. He posted several career-highs in 2013-14, appearing in 81 games, tallying 17 points and averaging 11:09 in ice time.
The Blackhawks (37-21-5) are third in the Central Division with 79 points. The Sharks (30-25-8) are fifth in the Pacific Division with 68.
The NHL's trade deadline is 3 p.m. ET Monday.
- Mike Fiammetta