The Highland League minnows landed a dream tie after being paired with Rangers in Monday’s William Hill Scottish Cup fourth-round draw.
Their ground holds just 3,000 fans and Broch bosses now face a major decision on whether to stage the tie on home soil or move it to a bigger venue such as Aberdeen’s Pittodrie.
But Cowie hopes his men will be given the thumbs-up to run out on their own patch for what he described as the biggest game in the Fraserburgh’s history.
He said: “I’m still on cloud nine. I decided to get all the players together to watch the the draw because I had a feeling something was going to happen.
“The longer the draw went on the more we began to believe. We were all shouting for number 29 when our name finally came out - then our prayers were answered.
“It’s a massive draw for this club. Financially it will really help us out as you can imagine, in today’s world it is difficult to run a club.
“To know one of the biggest clubs in Britain coming up to play you is fantastic. If the TV came too that’d be unbelievable.
“The question now is, can we accommodate them? They have such a big support and for footballing reasons I’d love it to be here.
“But I understand that is a decision we will have to make as a club. If it has to be moved so be it.
“Whatever happens this is definitely the biggest game the club has ever seen.”
Gers are currently managerless after Pedro Caixinha was sacked last month.
And Cowie has backed his team of part-timers to heap more misery on the Ibrox outfit when the clash is played over the weekend of January 20-21.
“I’ve got guys in my side that will have to get the morning off work to play against Rangers,” he said. “I just hope their bosses are football men and understand.
“A lot of them are Rangers fans so they’ll be playing their heroes.
“But we have nothing to lose. Not one thing. It’s at home, so that gives us a chance. If a lot of things go in our favour, you never know what can happen.”
Meanwhile, Hearts and Hibernian will face each other in the cup for the third season running after being drawn together, while Celtic will kick off their defence of the trophy at home to Brechin.
Lanarkshire rivals Motherwell and Hamilton will also face off at Fir Park, while Kilmarnock will welcome Ross County to Rugby Park in another all-Ladbrokes Premiership showdown.
Last year’s runners-up Aberdeen host Championship high-flyers St Mirren, with St Johnstone facing Albion Rovers.
Dundee take on Inverness while Partick Thistle travel to the winner of Tuesday’s replay between Montrose and Queen of the South.