The team also made qualifying offers Monday to forwards Benn Ferriero, John McCarthy, Jamie McGinn and Frazer McLaren.
Desjardins appeared in 17 games with San Jose this past season, recording one goal and two assists. He also scored a goal in the playoffs. He also played in 58 games in the minors for San Jose's Worcester AHL affiliate, posting 12 goals and 17 assists.
Stalock earned the win in his first NHL game on Feb. 1 saving all nine shots as the Sharks overcame a three-goal deficit against Phoenix. Stalock injured his left leg three days later and had season-ending surgery.