Lord Charles Powell said Thatcher, whose fevered hostility to Brussels in the latter part of her premiership led to her downfall in 1990, said she would have backed Cameron's new deal with the European Union.
Writing in The Sunday Times newspaper, Powell said Thatcher might have "raged more mightily" at Brussels than Cameron, the current Conservative leader and prime minister.
However, "She would have gone along with what is on offer, indeed negotiated something similar herself."
Thatcher stoked up animosity over Europe which helped wreck the premiership of her successor John Major as he tried to heal relations with Brussels.
"There were certainly times as prime minister when her frustration with Europe boiled over.
"The one thing I never heard her propose was Britain's withdrawal from the EU. Perhaps she would have persevered for longer before settling than the present prime minister and raged more mightily.
"But... I am confident she would have settled, and for something very close to what is on offer now."
However her close cabinet ally Lord Norman Tebbit slammed Powell's view.
Thatcher, Britain's prime minister from 1979 to 1990, died in 2013 aged 87.
Cameron is allowing his Conservative MPs to campaign to either leave or remain in the EU.
But he will be mindful that divisions over Europe ripped the party apart in the 1990s.
The Sunday Times said it had heard back from 144 Conservative lawmakers (330 sit in parliament), of which 66 said they were committed to leaving the EU, while 50 said they would vote to remain in the bloc.
In a letter to the broadsheet, representatives of 44 local Tory associations said Cameron had "undermined" the goodwill of loyal members and warned him: "No prime minister has a divine right to rule."
A Downing Street spokesman said Cameron was "simply making the point that everyone should ultimately vote with their conscience.
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