On October 10, 2020, Thompson as a free agent was signed to a one-year, $750,000 contract with the Winnipeg Jets, marking his ninth NHL club. Out of respect for the late Rick Rypien, who would have played with the Jets wearing #11, Thompson chose the number for his jersey, becoming the first player to do so since the Jets franchise relocated from Atlanta. Later, on February 25th, 2021- Thompson scored his first goal as a Winnipeg Jet- the game-winner- in a 6-3 Jets victory over the Montreal Canadiens- one of his former teams.