keep a wary eye on (someone or something)

To observe or monitor someone or something very carefully or cautiously, as in expectation of a negative or detrimental outcome. Despite the government's optimism, analysts are keeping a wary eye on the economy as tensions abroad threaten to bring turbulence to the stock market. I couldn't tell you why exactly, but I never trusted Jake. I always kept a wary eye on him when he was in the office. We'll have to keep a wary eye on the weather. We'll get stuck out here if it starts snowing too heavily.