The Prime Minister will agree the names of the nominees for the posts when he meets Romano Prodi, the president-designate of the European Commission on 14 April, Downing Street sources confirmed.
The mass resignation of the Commission in response to allegations of fraud and mismanagement has accelerated the need to agree a new team under Mr Prodi.
The need for urgent reappointments could rule out Chris Patten, the former governor of Hong Kong who will be committed to chairing the commission on the future of the Royal Ulster Constabulary until the summer.
There are strong, though unconfirmed reports at Westminster, that Mr Blair has agreed to accept Sir Alastair, who was nominated by William Hague, the Conservative leader.
But Ian Taylor, a former minister with expertise in information technology, is a strong late contender.
Neil Kinnock, the Labour transport commissioner, will have his term renewed, but under new rules. Mr Prodi has more power over the selection of his new Commission team and although he is expected to accept Mr Blair's nominations, he can negotiate to ensure they are the right choice for the portfolios he has in mind.
In a break with the past, Mr Prodi is expecting a list of candidates from Mr Blair and other leaders, rather than two firm nominations.
Downing Street sources confirmed that it was likely the choice would be made at the meeting with Mr Prodi on 14 April. Mr Prodi, who was selected at the Berlin summit and must be endorsed by the European Parliament, wants the commissioners to be in place the summer, although their term of office formally starts in December.
There is growing criticism among some pro-euro MPs at the failure of the Britain in Europe campaign by Lord Marshall of Knightsbridge, the president of British Airways, to make more impact against the anti-euro campaign, Business for Sterling. One pro-euro MP said: "There are a lot of tensions within the pro-euro campaign.
"It's really got off to a pretty chaotic start and at this rate, it could wreck the chances of holding a referendum."
The anti-euro campaigners claim their opponents' campaign was stalled by the launch coinciding with the call by the former German finance minister, Oskar Lafontaine, for tax harmonisation across Europe. The appointment of Judith Mayhew from the London Corporation to the board of the pro-euro campaign was aborted after protests over its neutrality being undermined.
Pro-euro MPs said the Britain in Europe campaign for the single currency had been badly handled, but one supporter at Westminster said: "It's not going anywhere but it doesn't matter.
"We are keeping our powder dry until after the European elections are over. Then we will begin."
There is an uneasy truce among pro-euro Tory MPs, led by Kenneth Clarke and Michael Heseltine, until after the elections on 10 June.
"If William Hague tightens up the euro position, some of us will come out fighting," said a senior Tory. "We have said to him, `Just keep your mouth shut.' If Hague decides to make it an election issue, there will be a split in the party."Reuse content