Shares in the LSE hit an all-time high on Tuesday following the reports.
Click here to see a graph of LSE's share price.
The LSE, which floated at 365p a share in July of last year, saw its share price rise to 445p as Europe's markets reopened following the Easter break.
Failed take-over
A planned merger between the two exchanges was cancelled in September 2000, when the LSE withdrew from the proposed tie-up in order to fight off a take-over bid from the owner of the Stockholm stock exchange, OM Gruppen.
But even before the merger was called off, there had been stiff resistance from some shareholders in Frankfurt and London, who feared that their respective market would lose out in the deal.
Shares also rose in the pan-European bourse Euronext, which is also expected to enter any battle for LSE.
Euronext scored a coup over its London rival in November when it snatched the London futures and options exchange Liffe from under the LSE's nose.
Shares in Deutsche Bourse were up 0.5% to 47.55 euros in early trading in Frankfurt.
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