Mr Thorpe was acquitted of conspiracy to murder his alleged former lover Norman Scott in 1979.
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The Lib Dems director of campaigns Nick Harvey MP has nominated Mr Thorpe to go forward for election in a ballot of party members to be held next month.
If Mr Thorpe polls well, then Lib Dem leader Charles Kennedy will be under pressure from party members to nominate him for a life peerage when the next opportunity arises.
However, the party is deeply divided over whether Mr Thorpe deserves a peerage.
Many feel he is still disgraced, and that as he is suffering from Parkinson's disease he would not be an effective member of the reformed House of Lords.
But there is an equally strong body of opinion that believes that Mr Thorpe has suffered enough and deserves the recognition of a peerage.
Leader for nine years
Mr Thorpe led the Liberal Party for nine years, after succeeding Jo Grimond as leader in 1967.
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When an affectionate letter between the pair appeared in the press, Mr Thorpe resigned as leader.
Claims that a man was hired to kill Mr Scott led to the conspiracy charge at the Central Criminal Court. Mr Thorpe was acquitted in 1979.
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