Sturm, 26, has nine goals, eight assists with a minus-5 rating in 53 games this season for the Wild, mostly on the fourth line. The native of Germany was signed as a college free agent out of Clarkson in 2019. Sturm won 51.1% of his career faceoffs, compared to just 39.5% for Jost.
Jost, 24, has six goals, eight assists and a plus-1 rating in 59 games this season. He was a first-round draft pick by the Avalanche in 2016 out of North Dakota.
Sturm can become an unrestricted free agent this summer. Jost is under contract for next season with a salary-cap hit of $2 million.
The Avalanche, who are firmly in control of first place in the Central Division, acquired veteran defenseman Josh Manson on Monday in a trade with Anaheim.