The billionaire investor believes it is inappropriate for Tritton, who used to work at Nordstrom from 2009 to 2016, to be deciding compensation for Nordstrom family members who are executives at the company, as he used to work around them, according to WSJ.
Cohen has previously traveled to Seattle, where Nordstrom is based, to meet with members of the family and learn more about the business, WSJ said.
Both Cohen and Nordstrom did not immediately respond to Reuters requests for comment.
The department store chain in September last year adopted a "poison pill" to prevent investors from amassing 10% or more of its shares, after Mexican department store chain Liverpool (LIVEPOLC1.MX) disclosed a 9.9% passive stake in Nordstrom.
Cohen also had a 9.8% stake in Bed Bath & Beyond, which he sold in August, following a stunning rally in the stock.