keep close watch on
keep (a) close watch on somebody/somethingalso keep (a) close watch over somebody/something
to guard or follow carefully someone or something With an international team keeping close watch on polling stations, voters chose from an array of 12 candidates. Republicans are warning the president to keep a close watch on spending.Related vocabulary: keep an eye out (for somebody/something)
Usage notes: sometimes used in the form keep a watch on: He wants to keep a watch on who comes and goes from the office.