U.S. Immigration and Customs Enforcement is tracking charges of child pornography and solicitation of sex from a teenage girl against Pittsburgh Pirates pitcher Felipe Vázquez, agency officials said Thursday, raising the possibility that the U.S. will seek to deport the All-Star closer if he is convicted of crimes.

But removing him to his native Venezuela may prove difficult for the U.S., amid political instability there and all-but-severed U.S. relations with the government of Nicolás Maduro. Vázquez could, in turn, face...