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The fears are understood to run right to the top within the LSE's senior management team, which includes chief executive Clara Furse, in addition to its well-connected court of advisers.
It is feared that although Nasdaq is unlikely to shut down Aim altogether, it could easily choose not to support it and could scrap LSE's investment plans for the future.
Although no figures on the amount the LSE spends investing on Aim are available, it is one of the most high-profile parts of the LSE, with recent marketing trips to China and Vancouver.
According to the latest statistics, it was home to 1,590 companies at the end of September, and companies listing on it have raised £34.3bn since its launch in June 1995.
The market offers growing companies, and an increasing amount of international companies, the chance to list on a regulated exchange with less stringent regulation than those applied on the LSE's Official List.
But the LSE is understood to be increasingly fearful that were Nasdaq to successfully make a bid for the LSE, Aim's 'light touch' could well turn out to be its downfall. Of particular concern are recent comments made by Nasdaq chief executive Bob Greifeld, in which he appears to disparage junior markets in general.
Speaking last month at the Boston College Chief Executives' Club, he said Nasdaq's efforts to encourage foreign companies to list had been hampered by the onerous Sarbanes-Oxley regulations.
'One of the unintended consequences of Sarbanes-Oxley is that we see a global race to the bottom with respect to regulatory standards,' he said.
In the speech, he said he was aware of the appeal of exchanges like Aim but said the answer was to maintain high standards to avoid blunt new regulations. Those comments, mixed with earlier ones made by the Nasdaq chief, have sparked the current fears.
One LSE insider said: 'He (Greifeld) appears to suggest the success of Aim is part of a 'race to the bottom' that he doesn't like, and that is the basis of concern.'
Others within the exchange and its wider community believe Nasdaq may strangle Aim, by keeping it as it is but diverting all new business to Nasdaq. An LSE spokesman declined to comment.
The whole issue remains hypothetical until Nasdaq, which owns a 25.3pc stake in the LSE, tables a bid for the British exchange. Its initial 950p-a-share approach was rejected in March, and Mr Greifeld is understood to be more than willing to wait until early next year rather than launching a rushed bid now.
A Nasdaq spokesman declined to comment.
By James Quinn, Business Correspondent