Charlotte Street is off George Street, close to North Bridge.
Det Insp Andy Crawforth said: “Following reports of two men entering the water, a search was immediately launched to locate and identify them.
“We are extremely concerned for their welfare and are conducting extensive lines of enquiries in an attempt to identify and locate them.”
Det Insp Crawforth said there would be an increased police presence in the area over the weekend.
He added: “To help with these enquiries, I would ask anyone who believes they know who these men are, or who thinks that someone they know went missing yesterday evening, to contact us immediately.”
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