The Premier League side confirmed on Wednesday the English Football League has been asked for dispensation to play the match at a neutral venue.
Spurs have experienced delays with the major rebuilding project at White Hart Lane and Wembley, their temporary home, is unavailable on the week commencing September 24.
The club acknowledged in a statement that Milton Keynes, some 50 miles north-west of White Hart Lane, “may not be an ideal destination for every fan to get to on a weekday evening”.
But Stadium MK, the home of League Two side MK Dons, is a particularly divisive choice due to the controversial history of the club.
Wimbledon, FA Cup winners in 1988, were uprooted to Milton Keynes from south London in September 2003, in what was an unprecedented move in English football history.
Fans protested against the switch and formed a new club, AFC Wimbledon, who have risen through the non-league pyramid and now play in League One.
“We appreciate it was always going to be difficult to find a suitable venue within [the] parameters,” THST said in a statement.
“As a supporters’ organisation, we would obviously not be happy to see our club’s home games moved to Stadium MK.
“Should the game go ahead, we would urge fans to consider the history of the MK club and the views of our friends at AFC Wimbledon.
“Board members of THST will not be attending the match if it is played at Stadium MK.”
A THST survey found 70 per cent of fans wanted the tie to be played within the M25 motorway, a rough border of London, with 46 per cent preferring to find an alternative ‘home’ venue rather than playing the game at Vicarage Road.
The EFL board will rule on Spurs’ application to play the tie at Stadium MK at its next meeting on September 6.