The comments came as the governor was asked about the topic during a press conference for a separate event.
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Behind the pictures of the potential shiny new facade remains an elusive price tag, and the unanswered question of who foots the bill.
"It looks beautiful, and obviously we want all of our professional teams to succeed in Illinois," Pritzker said.
Despite seeming impressed with the renderings of an open-aired, half translucent ballpark, Pritzker voiced concerns about how the plan would be funded.
"We need to be careful about how we use public dollars," Pritzker said.
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The governor said his staff may meet with the White Sox and developer, Related Midwest, soon to hear the pitch and a plan for how it would affect Illinois residents.
"Taxpayer dollars are precious, and so the question really is, what benefit financially are they bringing fiscally to the state and the city and the county?" Pritzker said.
The new complex would consist of the stadium, open park spaces and apartment buildings.
Gov. Pritzker voices taxpayer funding concerns on Sox stadium proposal
This new ballpark would move the Sox from their longtime Bridgeport home to a more than 60-acre plot of land in Chicago's newest neighborhood known as "The 78."
The developer's images imagined riverfront baseball nestled between Roosevelt Road and 18th Street, which would add to Chicago's historic skyline.
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"The development would be a catalyst for the creation of Chicago's next great neighborhood, create tens of thousands of permanent and construction jobs and bring a state-of-the-art White Sox ballpark to the South Loop riverfront," Developer Related Midwest said in a statement.
Third Ward Alderwoman Pat Dowell supported the opportunity for growth, but also acknowledged the impact in traffic.
"The traffic impact on Roosevelt Road and 18th Street, security, and quality of life issues such as concert noise and pedestrian neighborhood access are just a few of the issues that will all have to be resolved," Dowell said last month.
Mayor Brandon Johnson and White Sox owner Jerry Reinsdorf said in a joint statement they discussed "the historic partnership between the team and Chicago and the team's ideas for remaining competitive in Chicago in perpetuity".
The White Sox are the second professional sports team, alongside the Chicago Bears, that Chicago leaders are scrambling to retain within city limits.