In a wide-ranging interview, Sir Ed was also pressed over his party’s position on Brexit.
In the 2019 general election, the Lib Dems stood on a platform to “stop Brexit” and saw its number of MPs fall to 11.
However, the issue has not featured prominently in the current campaign.
The party’s manifesto, which sets out what it would do if it wins the election, promises to “fix the UK’s broken relationship with Europe”.
It also says the party would seek to rejoin the single market, which allows goods, services and people to move freely between member states, with EU membership its “longer-term objective”.
Sir Ed was asked if the price of access to the EU market would be free movement of people.
“I don’t think the single market with free movement of labour is going to happen in the next Parliament,” he said.
“What I do think is going to happen is a good trade deal, certainly if the Liberal Democrats had our way.”
He insisted there was “a trade deal to be had which is short of the single market” but would also “tear up some of the red tape” and extra costs facing businesses.
The Lib Dem manifesto also promises to negotiate a Youth Mobility Scheme with the bloc, allowing Britons aged 18-35 to live and work in EU countries for up to three years and vice versa.
Pressed over whether this gave the message that accepting more European workers coming to the UK was a price he was willing to pay to improve relations with the EU, Sir Ed said: “I think immigration needs to come down.”
He pointed out the UK already has a Youth Mobility Scheme with countries including Korea, Japan and Australia.
However, he stressed the number of visas offered through any EU scheme would be capped so would not amount to free movement of labour.
