Citing a source, the Daily Herald claims the Hawks are in the market for a top-four defenseman, and have shifted their focus to Isles captain Mark Streit.
Streit, who is in the final year of his current contract, is also negotiating an extension with Chicago, but if talks break down, he could be moved before the deadline.
The Islanders are believed to be interested in young Blackhawks defenseman Dylan Olsen, who is playing in the AHL, and forward Jeremy Morin, who was recalled from the AHL on Saturday.
Nielsen is signed through the 2015-16 season and has an annual salary cap hit $2.75 million.
The Daily Herald suggests the Hawks might also be interested Buffalo Sabres blueliner Robyn Regehr, Colorado Avalanche defenseman Ryan O'Byrne, and Edmonton Oilers rearguards Mark Fistric and Ryan Whitney.
Phoenix Coyotes forward Boyd Gordon, Dallas Stars center Derek Roy and San Jose Sharks winger Ryane Clowe are also on Chicago's radar.