No dates were given at this stage for ties to be played but several Borders clubs have an interest in the early stages of the competition.
Tweedmouth Rangers, from Berwickshire, have a home tie in the first round against Edinburgh South and, if they get past the club from the capital successfully, they’ll have a trip to Bo’ness Athletic.
In the second round, Coldstream are due to face Livingston United at home, while Hawick Royal Albert United will travel to the capital to face the winners of the match between Edinburgh United and Leith.
Peebles Rovers are at home to West Calder United in the other second-round tie involving a Borders club.
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The draws for the Alex Jack Cup, and others, are due to be made at the East of Scotland Football Association’s annual general meeting on June 10.