Mr Lammy, the current shadow higher education minister, hopes to win one of the 19 places, which are elected by Labour MPs. The results will be announced on 7 October.
If he is successful, Ed Miliband could place the Tottenham MP in any brief, but he would not keep his current position as it is not a shadow Cabinet post.
Mr Miliband could then choose any other Labour MP to fill the role, which shadows David Willetts, the minister for universities and science.
Even if Mr Lammy is unsuccessful, Mr Miliband may still opt for a new face, given Mr Lammy's support in the leadership race for David Miliband, Ed's brother.
One MP being tipped for the job is Roberta Blackman-Woods, who before becoming an MP in 2005 was professor of social policy at Northumbria University.
Meanwhile, during fringe meetings at the party conference in Manchester, Mr Lammy conceded that Labour had not always got its approach right on the academy.
He said it had "not done enough" to communicate the importance of science to the public and had also failed to convince people about the importance of a 50 per cent participation rate in higher education.
However, he told conference delegates that the outcome of May's general election would hit the academy harder than any other publicly funded area due to the policy differences between the Conservatives and the Liberal Democrats.
"This is a time when the Labour Party has to step up and challenge the Liberal Democrats on the decisions they are about to make," he added.
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