Having not played against one another since September 2011, when Manchester United beat Leeds at Elland Road in the League Cup.
The old foes could go face to face in a friendly match at Perth's Optus Stadium next summer.
Manchester United are due to conduct their pre-season tour in Australia, with a match against A-League side Perth Glory already agreed.
Now, the Old Trafford club are trying to line up a match against Leeds United as another leg of the tour.
The dates for the fixture have also been earmarked; with United playing Perth Glory on 13 July, before facing Leeds on July 17.
Of course, this friendly match between United and Leeds could easily preceed their first top flight match since 2004, that is, if Leeds manage to secure promotion from the Championship at the end of the current campaign.
After playing United, Leeds will then travel to Sydney to face Western Sydney Wanderers for the opening of their new home ground in Parramatta on July 21.