Der Spiegel news weekly reported that Kengeter told Lars-Hendrik Roeller - an economic advisor to Chancellor Angela Merkel - in November 2015 that he was "basically in agreement" with the LSE over a planned merger.
Frankfurt prosecutors announced last week that they had opened a probe against the Deutsche Börse CEO on suspicion of insider trading after he bought around 4.5 million euros ($4.8 million) worth of his own firm's shares in December 2015.
Those shares increased sharply in value after the announcement of the LSE merger plans in February 2016.
Investigators say they suspect merger talks between executives at the two stock market operators in fact began in July or August 2015 and ran until early December.
Deutsche Börse says the shares were part of the normal executive pay programme - and that in any case, the two stock market operators did not open tie-up talks until January 2016.
Asked about the report in Der Spiegel, which did not cite any sources, a Deutsche Börse spokesman told AFP the operator was cooperating with the insider trading investigation.
A chancellery spokeswoman told AFP it does not comment on meetings held by Merkel's economic advisors.
The LSE-Deutsche Börse merger would create a financial markets behemoth competing with the likes of the Chicago Mercantile Exchange and ICE in the United States, as well as the Hong Kong stock exchange in Asia.
A tie-up would ring up one of the globe's biggest groups for stock listings and market data, creating competition fears among EU rivals.
LSE formally offered this week to sell clearing house LCH Clearnet SA to European rival Euronext if the European Commission approves the deal at the end of a competition probe.