An announcement could come after the Prime Minister Tony Blair speaks to new president of the European Commission, Jose Manuel Durao Barroso later today.
Mr Mandelson, one of Mr Blair's closest allies, has resigned twice from the Cabinet in controversial circumstances, most recently in 2001.
We spoke to the Liberal Democrats' Norman Baker and from Labour's Keith Vaz, a former Europe Minister Enlargement
If Mr Mandelson's appointment is confirmed, then it will prompt a by-election in Hartlepool - Mr Mandelson's constituency.
The appointment to the European Commission would come ahead of what could be a lengthy run-up to a referendum on the new European Constitution.
Britain's two current commissioners, ex-Labour leader Neil Kinnock and former Tory chairman Chris Patten, are stepping down.
EU enlargement means Britain will now have only one commissioner.
Speculation has been growing for weeks, but Downing Street has refused to confirm the reports.
If the appointment is made, it would signal a remarkable comeback for Mr Mandelson, who has been both trade and Northern Ireland Secretary.
He has twice resigned from the Cabinet in the controversy: over a home loan in 1998 and because of the Hinduja passports affair in 2001.
'Good names'
Mr Durao Barroso appeared to suggest he had asked for a list of possible nominees for the post from Mr Blair.
Asked whether he would find the nomination of Mr Mandelson acceptable, he told BBC's Newsnight: "Of course the process of selection ... it is the responsibility of the heads of government and the president of the Commission.
"So far I have not yet spoken to the prime minister of Great Britain about the Commissioner and I will not make any comment at this stage. "I hope that the prime minister of Britain presents me with good names because I think it is very important for Europe to have the best in the European Commission."
Mr Mandelson's appointment would delay the need for a Cabinet re-shuffle, at least until autumn, BBC political reporter Gary O'Donoghue said.
Hartlepool should be a safe seat for Labour, but after losing Leicester South to the Liberal Democrats and nearly losing Birmingham Hodge Hill in by-elections last week, the outcome is not being taken for granted, he added.
The Liberal Democrats have already printed material for a campaign in Hartlepool, according to the BBC's political correspondent Martha Kearney.
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I hope that the prime minister of Britain presents me with good names (for the post) because I think it is very important for Europe to have the best in the European Commission 
