Mr Blair initially expresses concern about changes to the electoral system because of Gordon Brown's reservations. But the dairy shows progress and agreement between the two leaders as the May 1997 election approached.
Speaking as extracts of his diaries are published in the press Mr Ashdown also claimed that Tony Blair is convinced of the case for proportional representation.
"But it isn't a question of whether we would have preferred this coalition or that.
"We would have preferred, and I would still prefer and I believe it will happen, to have a system of government in which parties co-operate and work together in the interests of the nation and the parties of the left make sure we have a better government."
Other claims in Mr Ashdown's journals include a secret pact between the two leaders to form a coalition government.
The journals, being serialised in The Times newspaper, show the extent to which Mr Ashdown had worked alongside Tony Blair, and reveal a strong personal relationship.
Mr Blair is said to have told Mr Ashdown discreetly he would back proportional representation and favoured having Liberal Democrats in his government whether or not Labour achieved a working majority in 1997.
'Paddy's dreams'
But problems would have arisen with such a scheme as Chancellor Gordon Brown is reported to strongly oppose PR.
While on Sunday, Deputy Prime Minister John Prescott told the BBC he would never have served in a coalition cabinet, saying the idea was in "Paddy's dreams".
In his diaries, Mr Ashdown recalls his involvement in secret talks with Mr Blair as early as 1993 - before he succeeded John Smith as Labour leader.
He catalogues their many discussions about forming a coalition government which would deliver PR.
Mr Blair initially expresses concern about changes to the electoral system because of Gordon Brown's reservations. But the dairy shows progress and agreement between the two leaders as the May 1997 election approached.
Mr Blair is said to have told Mr Ashdown on 14 January 1997 that "I have become convinced of the need for electoral reform in Britain".
Merger floated
Mr Blair even floated the idea of a merger of the two parties, says the journal, although that was quickly stamped on by leading figures in both camps.
It adds that the extent of co-operation between the parties was often discussed at Mr Blair's and Mr Ashdown's homes, with their wives party to the discussions.
Though actual co-operation has been much more limited since Labour came to power in May 1997, Mr Ashdown said he still believed that, eventually, the two parties would engage in coalition government.
Mr Ashdown told the paper: "The project was to design an aircraft which we believed could fly.
"What we have left is a blueprint for it to be done in the future, and two scale models in Wales and Scotland (the coalition pacts for the Welsh Assembly and Scottish Parliament) are already in the air."
The Prime Minister's official spokesman was dismissive of Mr Ashdown's diaries, saying it was a case of "another week, another book".
The spokesman said Mr Blair remained "unpersuaded" of the case for PR at Westminster.