The midlanders finished their group phase with a draw against league leaders Galway United.
Athlone Town have been handed a tough draw for the quarter finals of the All Island Cup.
Shelbourne will play host to the midlanders on the weekend of June 23rd.
Ciaran Kilduff's side emerged from their group phase in second position after Galway United pipped them to first on goal difference.
Galway will be at home to Treaty United, the only team remaining from Northern Ireland, Linfield, will host Wexford, while Shamrock Rovers take on Peamount United.
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