The new checks will require fingerprinting and facial recognition checks at all ports and airports.
Ylva Johansson, the EU's home affairs commissioner, had already announced a contingency plan of delaying until November 17, while still saying the change would happen on November 10.
The Guardian reports that UK transport operators were briefed by government officials last week to expect a further delay.
The EES was originally supposed to launch last summer, but France expressed concerns over its impact on this summer's Olympics.
It was then rescheduled for October 6, but then put back to November 10.
There are suggestions a “soft-launch” will be held on November 10, perhaps not involving all international routes.
Others have speculated the system could be launched just with facial recognition and not taking fingerprints.
The greatest congestion is expected to be felt at Dover, although Germany is also worried about delays at Frankfurt, Cologne and Munich airports.
The European Commission has not made any announcement on the matter.
Under the new regime, the EU will require non-EU nationals – which since Brexit includes those travelling on a British passport – to register biometric details, including fingerprints and a photograph, when entering a country in the Schengen area.
This new process will replace the current system of manually stamping passports when visitors arrive in the EU, and is intended to improve border security, combat illegal migration and prevent those without the relevant visas from overstaying.
On subsequent visits, once you have already been enrolled into EES, passport control officers will only verify your fingerprints and photo, which will take less time.
For full details on the new system, see here.
In August the government announced a new £10.5 million package of funding to help Eurotunnel, the Port of Dover and Eurostar prepare for the introduction of EES.