Reuters reports the US Federal Aviation Administration (FAA) is behind the move after the agency previously sought potential candidates from the three US airlines operating the Max.
In a statement, the FAA said a firm schedule had not yet been set for the simulator tests.
The Max line has been grounded since March following to fatal crashes involving the aircraft in just five months.
Last October, Lion Air flight 610 crashed into the Java Sea shortly after taking off from Jakarta, killing all 189 people onboard.
Five months later, in March this year, Ethiopian Airlines flight 302 came down en route to Nairobi. All 157 people onboard died.
Preliminary investigations suggest the same deep-seated flight control system was active when both aircraft crashes.
Boeing has since been working on a fix for the aircraft’s Manoeuvring Characteristics Augmentation System (MCAS). It is believed MCAS likely provided an incorrect reading from a faulty sensor, sending the aircraft into a nosedive the pilots could not recover.
Before the aircraft can return to service, the fix and any alterations to pilot training or manuals will have to be signed off by the FAA.
Boeing scaled back production of the Max in April, but is reportedly now looking to scale this up from February next year.
The Max grounding has had a major impact on the aviation sector this summer, the effects of which will linger into many airlines winter schedules.
Comparing 737 Max schedules from mid-February versus early-August, flight schedule analyst OAG found scheduled 737 Max capacity had fallen 41 million seats from 62.7 million to just shy of 21.4 million.
Tui, which has 15 Maxs, said the impact would run to around €300 million.
Norwegian, which operates 18 Maxs, was forced to combine a number of transatlantic services and wetlease replacement aircraft at significant expense to mitigate the effects of the grounding.
It has since announced plans to pull its Irish transatlantic operation from 15 September, citing the Max grounding.
Ryanair, which has 135 Maxs on order, the first of which had been due for delivery this year, is now unlikely to receive its first new Max aircraft until the New Year.
This has forced the budget carrier to cut its planned rate of growth for summer 2020 from 7% to 3%, with its full-year traffic through March 2021 likely to come in some five million passengers below where it previously estimated.
Ryanair says it will be forced to cut jobs, routes and bases as a result.
China Southern, meanwhile, has suspended its order for 64 Maxs.
Boeing still has a backlog of about 5,000 Max orders. At the Paris airshow, British Airways owner IAG gave the plane maker its most public backing, signing a letter of intent for an order of 200 Max aircraft.
