Certification flights for the Boeing 737 Max are likely to be conducted in October following approval of the software update to the plane's anti-stall device implicated in two fatal crashes, according to news reports.

But the US Federal Aviation Administration, or FAA, said there is no schedule to return Max jets to service and declined to comment on the news reports.

"The certification flights are part of the return to service, so we aren't going to speculate on when they will occur," Lynn Lunsford, a spokeswoman for the FAA, told China Daily.

Boeing also declined to comment on the scheduling of the certification flights for the updated Max jet. Peter Pedraza, a spokesman for Boeing, told China Daily: "There has been no change to our best estimate of a return to service in the early fourth quarter, and progress in the software continues to support that time frame."

As for test flights, Bloomberg, citing "people briefed on the matter", said conducting them in October would be consistent with Boeing's plan to return Max jets to service by the fourth quarter.

The Seattle Times reported that the FAA plans to issue standards for pilot training in September. If the Max is cleared to return to service, the newspaper said Boeing plans to increase production to 52 planes a month by February 2020 and to 57 planes a month by next summer. Boeing cut production to 42 planes a month after the worldwide grounding in March.

Boeing and the FAA have been criticized since fatal Max crashes in Indonesia in October and Ethiopia on March 10. A total of 346 passengers and crew were killed. The FAA was the last regulator to ground the 737 Max. China's regulators were the first.

American Airlines said it has canceled Max flights through Nov 2 and will follow FAA directives. Analysts estimate it will take at least 45 days to return the grounded aircraft to service after receiving regulatory approval.

"According to Boeing, they will submit their final certification package to the FAA in September," American Airlines told China Daily. "Once submitted, the FAA will determine when the Max returns to service in collaboration with other global regulators."