Namestnikov, who signed a one-year, $2.5 million contract with the Lightning on July 13, can become an unrestricted free agent after the season. The 30-year-old forward has 15 points (six goals, nine assists) in 57 games.
The Lightning will retain 50 percent of Namestnikov's salary.
Selected by Tampa Bay in the first round (No. 27) of the 2011 NHL Draft, Namestnikov has 251 points (113 goals, 138 assists) in 610 regular-season games with the Lightning, New York Rangers, Ottawa Senators, Colorado Avalanche, Detroit Red Wings and Dallas Stars. He has 11 points (six goals, five assists) in 48 Stanley Cup Playoff games.
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Eyssimont, who was claimed off waivers from the Winnipeg Jets on Jan. 6, is in the final season of a two-year, $1.5 million contract he signed on July 28, 2021. He can become a restricted free agent after the season.
The 26-year-old forward was selected by the Los Angeles Kings in the fifth-round pick (No. 142) of the 2016 NHL Draft. He has 13 points (four goals, nine assists) in 39 games as a rookie this season.
The Lightning (37-19-4) are in third place in the Atlantic Division, four points behind the Toronto Maple Leafs for second. They previously acquired forward Tanner Jeannot from the Nashville Predators for defenseman Cal Foote and five draft picks on Feb. 26.
The Sharks (18-31-12) are in seventh place in the Pacific Division, one point ahead of the Anaheim Ducks and Chicago Blackhawks for last in the Western Conference, and two points ahead of the Columbus Blue Jackets for last in the NHL.