Dame Judi won an Oscar for Shakespeare in Love
In a letter of support to one of the chief critics of the changes, Dame Judi, an RSC honorary associate artist, stated she was "deeply worried" about its future, the paper reported.
Cordula Kempe, artistic director of the charitable trust the Rudolph Kempe Society, has submitted a 22-page report on the adverse affects the plans will have on the acting profession.
The overhaul could see the RSC quit its home at the Barbican in London and change the way acting contracts are offered, with job losses expected.
Dame Judi wrote to Ms Kempe to agree with her concerns about the proposed changes to the RSC's Stratford-upon-Avon site and the restructuring of the company under the stewardship of artistic director Adrian Noble.
The paper reports Dame Judi wrote: "I applaud your submission to the RSC governors and you have my wholehearted support.
"I am deeply worried about what is happening, as I know are so many people in the profession."
Flexible
Noble, who is directing the West End musical Chitty Chitty Bang Bang, has come under increasing pressure over his proposals which include introducing shorter contracts and creating three repertory companies.
The RSC's argument is that the company needs to be more flexible and big-name actors will be attracted by shorter contracts.
There are also major concerns about the £100m project to build a new theatre village at the site of the Royal Shakespeare Theatre in Warwickshire.
Ms Kempe has written to Noble and the RSC governors that concern about the RSC changes "seems to be shared by an overwhelming majority of senior members of the theatrical profession".
The main fears about the rebuilding project at the Royal Shakespeare Theatre is the "uncertainty" surrounding it in both artistic and financial terms.
Politicians at the recent Commons Culture, Media and Sport Committee also raised doubts that the £100m project may be too much of a financial risk.
But it did say the RSC had made a good argument for the demolition of the current 1930s-built theatre.
The proposal is part of the raft of plans designed to create a "waterfront village theatre" in Stratford.
Plans include: