Monday's game was called off because of fog in Perth and the SPL is keen for postponed fixtures to be played at the earliest available date.
But this weekend's free dates, created by the international break, do not suit the Dons, who have four players away on international duty.
Josh Magennis, Peter Pawlett, Mohammed Chalali and Ryan Jack are unavailable.
Magennis and Pawlett are on Under-21 duty for Northern Ireland and Scotland respectively, while Mohammed Chalali is with Algeria's Under-23 Olympic squad.
Jack is also on international duty, although he would be suspended for the Saints fixture if it were played this weekend.
SPL chief executive Neil Doncaster told BBC Scotland on Monday evening that his preference was for the clubs to get the game played soon, but he stressed there was no way of insisting that it be staged this weekend, given the short notice for the clubs.
"We'd like it played as soon as possible because we know what the issues were last year and the year before in terms of fixture congestion," Doncaster said.
"The last thing you need is fixtures piling up at this stage of the season. The earlier we can get a fixture away, the better."