Thornton and Nash played for Davos during the 2004-05 NHL lockout, and TFP has learned that both players are leaving this week.
Earlier today, Sharks center Logan Couture agreed to terms with Geneve-Servette HC, also of the Swiss league.
Thornton, 33, tallied 18 goals and 59 assists for 77 points in 82 games with the Sharks last season.
Nash, 28, registered 30 goals and 29 assists for 59 points in 82 games with the Columbus Blue Jackets last season. He was traded to the Rangers on July 23.