The body believes that, following devolution, Wales should no longer have a voice at Westminster in addition to having its own elected Welsh Assembly.
In a new report, the Constitution Unit has said that devolution will have failed if there is still a Secretary of State for Wales in the Cabinet in five years time.
The body believes that, following devolution, Wales should no longer have a voice at Westminster in addition to having its own elected Welsh Assembly.
And it argues that the posts of Welsh, Scottish and Northern Irish Secretaries should disappear.
The revelations are the latest volleys in a long-running debate over how long the post will continue to exist.
Earlier this month current Welsh Secretary Paul Murphy said Labour had no plans to scrap the post after the election.
Hague challenge
Mr Murphy told MPs that the role was part of the devolution settlement and - despite speculation to the contrary - would remain.
But, he admitted, ultimately it was a decision for Prime Minister Tony Blair.
Mr Murphy's comments came in response to a challenge issued by the Conservatives to guarantee that the post would not be abolished.
The future of the title "Secretary of State for Wales" featured prominently during the annual Welsh day debate in the Commons.
The Conservatives promised they would keep the role but would combine it with another cabinet post to reflect the changes brought by devolution.
The comments of the Constitution Unit will undoubtedly set the controversial debate blazing again.
Professor Robert Hazell, has said government policy on devolution is fragmented enough already.
He has called for a new Secretary of State for the Union, who could take a more rounded view of what he says are the unresolved issues of finance and representation at Westminster.
The future of the post has been a subject for debate in all parties since most of the Welsh Secretary's powers transferred to the National Assembly for Wales in 1999.
There had been speculation that the Tories would scrap the role if they won the election.
Whitehall insiders believe Tony Blair may merge the Welsh post with its equivalent in Scotland and Northern Ireland to create a new Department for the Nations, if Labour wins the next election.