The request was submitted ahead of Thursday's draw, which saw Spurs given a home tie, and will be considered by the EFL at its next meeting on September 6.
Tottenham's game is scheduled to be played in the week commencing September 24, but their new stadium will not yet be ready and Wembley is unavailable due to Anthony Joshua's heavyweight fight with Alexander Povetkin on September 22.
As a result, Spurs have been forced to consider alternative options and have settled on playing at the 30,500-capacity home of MK Dons in Milton Keynes.
"We appreciate that Stadium MK may not be an ideal destination for every fan to get to on a weekday evening," Spurs said in a statement. "However, the club felt it would not be beneficial to request a reverse of the fixture as it would have resulted in no more than a 10% allocation of tickets for our supporters at the venue of our opponents.
"In contrast, we shall have a ticket allocation of up to 90 per cent at a neutral venue, ensuring greater access for our fans.
"Consideration was given to a number of different football stadia and for a variety of reasons - capacity, availability, facilities, accessibility, pitch quality and clubs still being in the competition themselves - it was simply not possible to secure a neutral venue within the M25.
"We are extremely conscious of having to ask our supporters to attend home matches at more than one venue and apologise for any inconvenience this may cause. Further details regarding the scheduling of our tie, along with ticketing, will follow in due course."
Spurs announced this month that their highly-anticipated move into the new Tottenham Hotspur Stadium has been put back until at least the end of October.