Woo added that while the Hawks are shopping Schroder, the market has been tepid due to "concerns about his attitude" and the fact that he has $46 million remaining on his contract.
The 24-year-old native of Germany is coming off his most productive season, as he averaged 19.4 points, 6.2 assists and 3.1 rebounds per game while shooting 43.6 percent from the field and 29.0 percent from beyond the arc.
He was by far the best player on a Hawks team that went 24-58 last season after being gutted via free agency and trades.
While Schroder seems like a good fit for a rebuilding team like the Hawks in theory because of his production and young age, there are some issues that may be forcing Atlanta's hand.
Last month, Schroder unfollowed the Hawks on Instagram and deleted every post he made that referenced the organization.
Additionally, Michael Cunningham of the Atlanta Journal-Constitution reported in March that it has been recommended that felony aggravated battery charges be levied against Schroder and three other men stemming from a September fight in a shopping center parking lot.
Woo speculated that the Hawks may have to package Schroder with some picks to move him.
Atlanta doesn't seem likely to move the No. 3 overall pick in the draft, but it also owns Nos. 19, 30 and 34.
Schroder figures to be a hot name in trade circles when the 2018 NBA draft emanates from the Barclays Center in Brooklyn, New York, on Thursday night.