The Hoops had moved into pole position for the Sporting Gijon hitman at the start of the week when they agreed a fee with the Spanish Second Division side.
Peter Lawwell and his negotiating team have been working for the past four days to personal terms with the 24-year-old attacker.
Manager Ronny Deila admitted the tall, powerful player ticked all the boxes for the man he wants to lead his line and provide the goal threat which was so sadly lacking in the Champions League play-off against NK Maribor.
The £3million package Celtic were prepared to pay would be the first money Deila has spent on a new signing since he took over from Neil Lennon two months ago.
The Hoops did manage to finally cut through all the red tape and get Wakaso Mubarak in yesterday, as first revealed on eveningtimes.co.uk
However, the Ghanaian winger is initially here on loan for a year, with Celtic holding an option to buy him from his Russian club, Rubin Kazan.
The Wakaso deal mirrors that which saw Jo Inge Berget arrive on loan from Cardiff and Aleksander Tonev from Aston Villa.
Jason Denayer has also been brought in on a season-long loan from Manchester City, but there is no right-to-buy attached to the deal for the 19-year-old Belgian defender.
Deila has insisted: "It must feel right in my stomach," before he will commit to a purchase, and forecast that it would only be in the final few days of the transfer window that the big business would be done.
In terms of outlay, Scepovic represents that big business.
But, in the wake of Celtic's failure to get into the Champions League, there now appears to be a serious risk he could join the list of players who got away from Celtic's grasp in recent weeks.
Haitian midfielder, Jeff Louis rejected the chance to move to Parkhead after the Hoops had agreed a price with his French club, Nancy.
Louis chose to move to Belgian club Standard Liege despite the fact Celtic claim their offer was more lucrative.
The Hoops were also reported to have been in the hunt to sign Polish striker, Lukasz Teodorczyk, but he has now completed his £3.6m move from Lech Poznan to Dinamo Kiev.
Missing out on Scepovic would be an even bigger blow to Deila than failing to get Louis as he has a much more pressing need to strengthen his attack than his midfield, which will be boosted when captain Scott Brown returns from his hamstring injury in the next few weeks.
With the transfer window set to close on Monday, and squads for the Europa League group stage scheduled to be submitted to Uefa, if Celtic need to move onto another target on their list at this late stage it will leave them exposed to auctions and inflated demands.