The federal parliamentary secretary from the ALP's powerful Victorian right faction said he made the approach last Wednesday.
"I did speak to the then deputy prime minister and say she should think about this," Mr Shorten said.
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"She gave it a great deal of serious reflection."
Mr Shorten said he became pessimistic about Labor's re-election chances during the past fortnight after speaking with voters in his Melbourne electorate of Maribyrnong.
"In terms of when, in the last two weeks I became very despondent about our chances of re-election," he said.
"Going around talking to voters, in Maribyrnong, in the disability sector - people said, `You can't just change your mind on climate change and leave a vacuum'."
The Rudd government had also failed to sell its resource super-profits tax, Mr Shorten said.
"They were saying, `We can see why mining companies should pay more money, but you haven't explained to us the detail of how it would work'," he said.
"We certainly hadn't explained it well. In terms of implementation, we hadn't engaged sufficiently with the business sector - that was crowding out all our other messages.
"So, I did think we had to do something."
Mr Shorten said taking down Mr Rudd was a decision the 112 members of the parliamentary Labor caucus took seriously.
"It is without a doubt the single hardest decision we have ever made in politics," he said.
"It wasn't done lightly.
"I concede it was done quickly and I can understand a fair amount of shock, but it wasn't done on the basis of an opinion poll."
Mr Shorten said Mr Rudd had been a very good prime minister.
