Ex-minister John Spellar is calling for Labour to scrap the post of deputy leader, arguing that the impending election contest will be too costly.
He estimates the ballot will cost the party - which is £23m in debt - £2m and would cost unions more than £1.5m.
He also believes the competition could be divisive within the party.
Alan Johnson, John Cruddas, Harriet Harman, Hilary Benn and Peter Hain are among seven MPs to officially declare, or indicate, an interest in the post.
Labour chairman Hazel Blears and Commons leader Jack Straw have also been mentioned as possible runners.
At Labour's conference John Prescott made it clear he intends to resign as deputy leader at the same time as Tony Blair leaves office - something which is due to happen by September.
But Mr Spellar told BBC Radio 4's PM the potential cost was "an awful lot of money to spend for the election".
He added: "At the same time we're also seeing cabinet members, almost by definition, having to distance themselves from each other...
"They should all be pulling together and quite frankly - not running campaigns, but running their departments and running the country.
"And this could go on until next summer."
He says his view has the unanimous support of local
activists in his constituency.
Mr Cruddas has said if he becomes deputy Labour leader he would not want the role of deputy prime
minister, saying he believes the role should be about providing a link between leadership and grassroots.