The firm, which provides water to around one in four people in Britain, is facing questions over its future, as it grapples with a £14bn debt pile.
“If evidence was required that privatising basic utilities hasn’t worked, this is it,” said Mr Khan.
“When things are good, their shareholders reap massive dividends. When they need investment, they make us pay more with our water bills. Well, there’s something wrong there, right?”
He added: “It’s a monopoly. What are you going to do? Change from Thames Water to somebody else? You can’t, right? They’ve got you over a barrel.
“That’s a failure of the Government not regulating monopolies, whether it’s Thames Water, or some of the train operating companies.”
Bringing water companies into public ownership is not Labour’s policy nationally, but Mr Khan said he was not in favour of nationalising Thames Water immediately.
“I don’t think we should be using our money to pay off shareholders. That’s not the best use of taxpayers’ money,” the mayor said.
“If it comes up to the contracts being renewed, like with the rail companies – yeah, nationalise them.”
A Government source clarified afterwards that, unlike train companies, water companies do not renew their contracts periodically, and instead hold indefinite licences to operate.
Mr Khan said City Hall has no powers of its own to bring Thames Water into public ownership, and that he would be concerned about taking over the company’s debts.
“If the Government was to – for example, theoretically speaking – write off all the debts, [and] allow us to keep the cash balances in Thames Water, I’d be interested,” he said.
Thames Water has said it has a “strong liquidity position including £4.4bn of cash and committed funding” and is working “constructively” with shareholders while keeping the regulator, Ofwat, informed of progress.
The company added that it “remains focused on delivering for our customers, the environment and stakeholders”.
If the firm cannot secure additional funding, it could be temporarily taken over by the Government until a new buyer is found, in a special administration regime (SAR).
A spokeswoman at the Department for the Environment, Food and Rural Affairs (DEFRA) said: “Ofwat monitors the financial position of all water companies, ensuring they take action when long term financial resilience needs to be strengthened.
“It is the role of regulators to scrutinise industry, which is why Ofwat continues to monitor the financial position of all water and wastewater companies.”