Federal Aviation Administration chief Steve Dickson, who will meet with Boeing's chief executive later on Thursday, is concerned the US airplane maker is pursuing a return-to-service schedule for the grounded 737 Max that is "not realistic," according to an email seen by Reuters.

Dickson will hold talks with CEO Dennis Muilenburg on the agency's review of the plane that was grounded in March after two fatal crashes in five months. The meeting comes a month after Boeing asserted it expected the agency would allow it to begin deliveries again in December.

In an email to congressional staff on Thursday disclosing the meeting and seen by Reuters, FAA official Philip Newman said Dickson is "concerned that Boeing continues to pursue a return-to-service schedule that is not realistic due to delays that have accumulated for a variety of reasons. More concerning, the administrator wants to directly address the perception that some of Boeing's public statements have been designed to force FAA into taking quicker action."

Dickson will make clear, the email added, "both the FAA and Boeing must take the time to get this process right."

The plane was grounded in March after crashes in Indonesia and Ethiopia killed 346 people.

On Wednesday, Dickson confirmed he would not unground the plane before the end of 2019. Boeing confirmed on Thursday the meeting would take place but did not elaborate.

Federal officials told Reuters earlier this week the FAA is not expected to authorize the plane to fly until January at the earliest, citing significant work still to be done. Some US officials think it may not be until at least February that Dickson gives the green light. Dickson told CNBC on Wednesday that Boeing had nearly a dozen milestones to meet before the plane could return to service.

The three US carriers that operate the 737 Max — Southwest Airlines, American Airlines, and United Airlines — are scheduling flights without use of the aircraft until early March 2020.

Southwest Airlines CEO Gary Kelly said on Thursday it is "likely" the airline will again need to push back the date.

Boeing said in November it expected the FAA to certify the 737 Max, issue an airworthiness directive and unground the plane in mid-December, even as it acknowledged it would not win approval for changes to pilot training until January. Boeing declined to comment this week on that forecast, deferring to the FAA.