According to the application, the site will be located at 100 Edison Drive.
The Level II license allows growing spaces for up to 3,000 square-feet.
Monroe city officials did not immediately return calls seeking comment.
Monroe does not have a marijuana moratorium, unlike other communities in Butler County, because City Council wanted to see how the new rules would develop across the state, city officials said earlier this year.
In June, City Manager Bill Brock said the inquiries Monroe received came from two representatives interested in building a growing facility of up to 25,000 square feet, and from a larger grower looking at a facility of up to 100,000 square feet.
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