A settlement deal that would have ended the probe was blocked by a court on Monday, leading Deutsche Boerse supervisory board chairman Joachim Faber to break off a trip to China and return to Frankfurt, the person said on Tuesday.
Kengeter, who denies any wrongdoing, made share purchases worth 4.5 million euros shortly before formal merger talks between Deutsche Boerse and the London Stock Exchange were announced in early 2016.
Deutsche Boerse and Kengeter have said he was authorised to buy the shares as part of his pay scheme at a fixed time, between Dec. 1 and Dec. 21, 2015.
"Faber is back and there will be a discussion on Thursday about what happens next," the source, who spoke on condition of anonymity due to the sensitivity of the matter, added.
Deutsche Boerse's shares extended losses to nearly 2 percent on Tuesday, making them the weakest performer in the 30-share DAX Index. The exchange operator is also due to report its quarterly results on Thursday.
Deutsche Boerse said on Monday a Frankfurt court had refused to ratify a settlement between the prosecutors, the exchange and Kengeter, whereby Deutsche Boerse had agreed to pay 10.5 million euros ($12 million) in fines, while Kengeter would pay 500,000 euros personally.
Frankfurt's public prosecutor said after the ruling that its investigation into Kengeter, which started early this year, could extend beyond next March.
Kengeter's contract as chief executive expires at the end of March 2018 and Deutsche Boerse has said it would not move to renew it until the insider trading case is settled.
"The investigations are continuing. Everything is possible: A termination of the investigation, an indictment, or also a new deal," the prosecutor's spokeswoman said.
Separate investigations by two other regulators are due to start only after the Frankfurt investigation is completed.
Further investigation could lead to a closure of proceedings due to lack of adequate evidence, or to an indictment, Deutsche Boerse said.
(Additional reporting by Andreas Cremer; Writing by Tom Sims and Douglas Busvine; Editing by David Evans/Greg Mahlich/Alexander Smith)
By Andreas Framke