Ms Thornberry made the claim as she outlined housing policy she would pursue if she was prime minister.
The Islington South and Finsbury MP told the Mirror she would offer a lottery of subsidised housing blocks to people in their 20s in every council area.
They would be charged half their salary for rent, theoretically helping them save for a deposit for home ownership using the other half of their salary.
However, they would be forced to move out when they turn 30.
Ms Thornberry told the paper: “We have to be radical and we have to be not afraid.
“People say: ‘Do you agree with everything in Jeremy’s manifesto?’ I say: ‘Yeah but it is a question of priorities.’ They also say: ‘Are you in any way more radical than Jeremy?’ Maybe I am in some ways, and when it comes to housing I am.
"And in my burning desire to sort out social care. I’m probably, you know, quite radical about that too.”
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Last month, Mr Corbyn led Labour to its worst election defeat since 1935.
Ms Thornberry remains the outsider in the party leadership race, with some bookmakers offering odds as long as 80/1. The other candidates are Sir Keir Starmer, Rebecca Long-Bailey and Lisa Nandy.