Mindful of placing undue stress on already stretched police resources, both clubs have shelved celebratory gatherings.
In the event of clinching the treble with a victory at Hampden tomorrow, Celtic had planned to present the trophy to fans at Parkhead on Saturday night.
However, that idea has now been scrapped along with a heroes and legends parade due to take place before a sell-out charity game at Parkhead on Sunday.
Aberdeen have also ditched plans for a public celebration should they win the Scottish Cup for the first time since 1990.
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Tradition has it that the Dons show off silverware to their fans with an open-top bus parade around the Granite City.
But with police and the army having to deal with a “critical” level of terror threat following Monday’s bomb attack in Manchester, the clubs have urged fans to respect the decision to cancel.
A Celtic statement read: “Given the situation and the pressure on police and security resources, we are sure that our supporters will fully understand these measures which have been taken.”
Celtic and Aberdeen have scrapped post-Scottish Cup final plans due to the Manchester bombings
Aberdeen chiefs also explained to their fans why the action had been taken.
A statement read: “In the event of Aberdeen being fortunate enough to win the Scottish Cup, the club would like to confirm that there will be no open-top bus parade on Sunday.
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“Given the situation and the pressure on police and security resources, we know our supporters will fully understand.”