Lanarkshire venues such as Motherwell’s Fir Park and Hamilton’s New Douglas Park are potential settings for the head to head in the third week of January.
Rovers secretary Paul Reilly will now head to Hampden as the club look to put a plan in place.
He said: “Obviously, we can’t stage the match at Cliftonhill, so we’ll attempt to find a solution which will allow as many people as possible to see it.
“It means so much to everyone at the club for a variety of reasons. The people of Coatbridge are excited and there is a big connection for the clubs through Jock Stein.
“It means a lot to everyone and the boys in the squad, as you would imagine, are very excited.
“There are a number of factors involved and this is the reason for the meeting with the SFA, just to clarify the position and see where we go from this point.”
Reilly added: “It wasn’t just the fact we won, it was the manner of the victory. To score with practically the last kick of the game with 10 men was unbelievable.
“It’s a huge, huge thing for Albion Rovers.”