It is feared that an army of maroon-clad supporters will head to Gorgie to meet the team bus after the Hampden Park showdown if Hearts are victorious over a struggling Celtic and bring home the silverware.
But the team will not be returning to Tynecastle Park and club bosses have pleaded with fans to adhere to strict coronavirus guidelines should Robbie Neilson’s team triumph in the William Hill-sponsored final.
Backing the plea, Chief Superintendent Mark Sutherland warned that “an appropriate policing plan will be in place”.
Officers have the power to break-up any mass gatherings and issue hefty fines. Those refusing to comply could find themselves in court.
Chief Supt Sutherland added: "The Scottish government strongly advise against gatherings in areas under level three restrictions. We would urge people to follow this guidance to help prevent the spread of coronavirus.
"The Chief Constable has been very clear that we are asking people to take personal responsibility to do the right thing and remember the purpose of these measures is to aid the collective effort to protect the NHS and save lives by preventing the virus from spreading.”
And he warned: "Our response will be measured and appropriate but we will use enforcement where required."
There will be no a victory parade if Hearts win but Edinburgh’s Lord Provost, Frank Ross has vowed one will be staged later.
He said: “Good luck to Hearts on Sunday.
"Like many I wish I could be there in person but I’m sure I’ll be joining tens of thousands watching and cheering safely from home.
“Whatever the result I’m sure they will do the city proud and I can promise, if they win the Cup on Sunday we’ll make sure they receive a fitting celebration when it is safe and permitted to do so.”
Hearts also urged supporters to enjoy the repeat of the 2018/19 final, which Celtic won 1-2, at home on TV.
The club said: “In years gone by, victorious cup finals have spawned momentous celebrations. Should the Jambos win at Hampden on Sunday then, as with most things this year, it will be different. In the event of a Hearts win we will be unable to have the traditional post-game celebrations, the team will not be travelling back to Tynecastle Park and there we will be no victory parade in the foreseeable future.
“It is vitally important that our fans continue to follow Scottish government guidelines with regards to social gatherings, for their safety and for those around them. On the advice of Police Scotland and supported by the club please do not travel to Hampden Park and please, no matter the final score, do not gather at Tynecastle Park.”
The club statement added: “If the Jam Tarts win the Scottish Cup for a ninth time then it will absolutely be cause for the Hearts family to celebrate. Please be assured that we will. At the very earliest opportunity and when it is safe for us all to come together, we will ensure we celebrate in style. Meanwhile, stay safe.”