Trump, a Republican, and his senior officials have said many migrants must be deported, blaming them, often in sweeping terms, for financial fraud and violent crimes.
Minnesota, which is governed by Democrats, has sued the Trump administration over the surge, which has sparked weeks of protests that led to the killings of two US citizens by federal agents.
Homan wants more jails in Minnesota to allow immigration agents to transfer custody of detained migrants. Some already do. Others, including the main jail in Minneapolis, do not cooperate.
Minneapolis and some other cities prohibit their employees, including police, from asking people about their citizenship or cooperating with federal immigration enforcement, saying it threatens public safety if migrants who are victims of or witnesses to crime are afraid to come forward.