Germany's ARD public television network and the "Süddeutsche Zeitung" (SZ) newspaper said Tuesday that Schindler would be replaced by 53-year-old Bruno Kahl, a senior ministerial aide to German Finance Minister Wolfgang Schäuble.
Schindler, a state jurist and government counter-terrorism expert, became BND chief in 2012. The ARD and SZ said the government had not confirmed the reported change - more than two years before Schindler's official retirement.
Kahl is a departmental director in the Federal Finance Ministry head by Schauble, who himself is a former interior minister.
Schindler has long pleaded for more technical and personal resources, and closer cooperation with European and American intelligence services.
Various reasons
ARD said various reasons were behind the reported reshuffle, including a major BND restructuring that will see the agency transfer many of 6,500 employees from Munich to a new Berlin headquarters by next year.
Chancellor Angela Merkel's chancellery had "forced" the change, claimed the SZ, which forms part of a investigative consortium with two of the ARD's regional channels, NDR and WDR.
An additional reason had been disclosures last year that the BND had used NSA search keywords to trace allied Europeans from the Bad Aibling surveillance station used by the BND and Americans near Munich.
Tiring scrutiny
The German news agency DPA last month quoted sources close to Schindler as saying scrutiny by German Bundestag parliamentarians amid the NSA scandal had had a tiring impact on the 63-year-old.
Since leaks in 2013 by the whistleblower and former NSA worker Edward Snowden, Schindler spent days being questioned by Bundestag inquiry committees and parliament's intelligence agency oversight committee, the so-called G10.
International cooperation vital
Last month, Schindler told the DPA news agency that international cooperation was vital to counter growing terror threats. "As the world grows more complex and trouble spots become more arduous it is more important than every to cooperate internationally," he said.
"No intelligence agency, even the largest, can scout the entire world. One needs regional partners," he added, while adding that Russia ran "very professional" secret services. "(Their) goal is to place Russia in a better light, and wreck and fragment European unity," he claimed.
(DW)