The memo suggested the Home Secretary wanted to introduce a cap of 75,000 a year with professionals and high-skilled migrants from wealthy countries such as Germany, Austria or the Netherlands allowed in only if they had a job offer and lower-skilled workers permitted to settle only if they were employed in posts where there was an identified shortage.
Last month, net migration jumped by 15,000 to an annual total of 182,000, well above the Coalition aim of having it below 100,000.
But Mr Clegg used his regular Whitehall press conference to pour ice water on the proposal, saying: "My advice to the Home Office is to spend less time leaking policies that are illegal and undeliverable and spend more time delivering on the policies we have agreed as a coalition; notably, the reinstatement of exit checks."
He said the leaked proposal to "pull up the drawbridge" on migration from other EU states would be a "disaster" for British business
Earlier, Ms May made clear reform of the right to free movement should form part of any negotiations on new arrangements for the UK's membership of the EU.
The leak was regarded as a classic pre-manifesto kite-flying exercise.
She said: "There is a growing concern about the way in which people can move freely across Europe."